/sci/ - Science & Math

>>10449989
80%

>>10450004
this

>>10450004
>>10450008
OH NO NO NO NO
The absolute state of brainlets on this board.

>>10450012
Okay, 96%

>>10449989
41.38%

>>10450012
but there are blue taxis in carborough
and witnesses are right 80% of the time
the fact blue cars make up 15% of the taxis should not influence the probability of the witness being right because blue cars do exist in carborough

>>10450032
OH NO NO NO NO SOMEONE TAKE HIS SHOELACES

>>10449989
zero, taxis are yellow

>>10450039
https://plus.maths.org/content/solution-taxi-problem
But that's actually the solution.

>>10450041
but prompt says 15% are blue

>>10450045
Okay, so
>>10450034

>>10449989
i fucking hate probability, could never get it to click fml

>>10450041
Is there a way to solve this without considering 100 possible cases? My math is really rusty.

>>10450056
It's just simple division man! I believe in you!

Do the four possible cases, consider the two which could occur according to the information, and do the calculation.

>>10450049
Ah I feel you Anon. It's been a while since I've done this but after some reading and diagramming I've returned to the intuition for this problem. There are four cases: taxi is blue and witness is right or wrong, or taxi is green and witness is right or wrong. Once this enumeration, the problem should fall into place.

>>10450092
There's gotta be a formula, an algebraic way. Considering cases makes me uneasy.

>>10449989
If they mean witness are correct 80% of the time they say a they saw a blue taxi then the answer is 80%.

If they mean witnesses are correct 80% of the time they report a taxi is blue or green then the question can't be answered without more information.

>>10450108

>>10450041
This is incorrect. It says 0.8 is the chance that a witness will report blue given the taxi is blue. But the problem in the OP is worded so that 0.8 is the probability that a taxi will be blue given the witness reported they saw a blue taxi (or the chance that a witness will be correct given they report they saw a taxi of a certain color, the question is ambiguously worded).

>>10450101
I think there is but it's more confusing in my opinion; always had trouble parsing the grammar of "given" in problems; bad-juju, mang. Just mindlessly list and then use your brain to match cases with the problem; sum and divide. The answer I got was .21: either the taxi was blue and the witness was right (.15*.8) or (+) it was green and they were wrong (.85*.2).
>>10450048
You've got your taxi color probabilities reversed, he says.

>>10450113
>witnesses are correct 80% of the time when making such statements

This means P(the taxi is blue | the witness reported the taxi is blue) = 0.8

It does not mean P(the witness reported a blue taxi | the taxi is blue) = 0.8

>>10450121
yeah it's a trick question that's literally answered itself

>>10450092
Shouldn't there be only one scenario we care about because the question asks for the possibility of a blue taxi being tge criminal? The taxi is blue and the witness is right? Is there a way to solve it just using that information? This is the only way that makes sense to me.

.8*.15
12%
+
.2*.85
17%
Total chance: 12+17=29%

>>10450126

>>10450092
>diagramming
ya, i remember always having to draw everything out in order to solve even the simplest question, felt borderline retarded when some of my classmates could do it in their heads. only upside is the teachers always said probability is counterintuitive

>>10450126
>they're right 80% of the time 29% of the time

>>10450034
Seems correct to me.
Out of four possible outcomes:
1. Witness is correct, taxi is blue
2. Witness is correct, taxi is green.
3. Witness is wrong, taxi is blue.
4. Witness is wrong, taxi is green.

Now the witness claims to see the blue taxi. Therefore only 1 and 4 are possible.
We want to know the probability of blue taxi being involved, that is outcome 1.
P = (.8*.15)/(.8*.15+.2*.85) = .41

>>10450150
0.8 is the probability of the witness being correct when they make such a statement. You are treating 0.8 as the probability of a witness reporting a blue car given the car is blue.

>>10450160
and the difference is....?

>>10450210
P(the car is x | the witness said the car is x) = 0.8

P(the witness said the car is blue | the car is blue) is not known.

>>10449989
>Surely you are not so dumb as to be unable to solve this simple problem.
Since eyewitness accounts are notoriously unreliable, I pump the witness for more information about the alleged taxicab. Several times at random during the interview I ask the witness about the color of the taxi; sometimes I ask him "so it was a YELLOW taxi, right"? Eventually the witness slips up and shows that he's confused about what he saw and he doesn't really have a clear memory at all about what he saw. Then I discount the so-called 'eyewitness' account and go back to actually investigating the crime instead of worrying about some stupid-ass math problem.

>>10450215
give a concrete example of the different results, in the case of
100 cabs total,
15% blue cabs
80% witness accuracy, vs the other kind

>>10450034
>>10450150
This.


Think of it as 100 taxis.
15 are blue.
85 are green.

Blue taxi, correct witness = 15 x .8 = 12
Blue taxi, wrong witness = 15 x .2 = 3
Green taxi, correct witness = 85 x .8 = 68
Green taxi, wrong witness = 85 x .2 = 17
If you sum them you get 100.

The question asks for the probability a blue taxi was involved in the crime.
That means the probability the witness said it was a blue taxi and it was a blue taxi.
The only other option if he said it was a blue taxi would be if he was wrong and it was a green taxi.

So we have:
(BTC) Blue taxi, correct = 12
(GTW) Green taxi, wrong = 17
Total = BTC + GTW
Thus, the probability of it being blue and correct of these only two possible outcomes (since he said it was blue) is:

BTC / (Total)
12 / (12 + 17)
41.38%

Thank you for coming to my TED Talk.

>>10450237
The middle two are eliminated because:
If it was a blue taxi, the witness wouldn't be wrong.
If it was a green taxi, the witness wouldn't be correct.

>>10450229
If by "witness are correct 80% of the time when making such statements" they mean the witness is correct 80% of the time they say they saw a blue taxi then the answer is 80% and the other information given is unnecessary. If they mean the witness is correct 80% of the time they say they saw a blue taxi or a green taxi then

0.8 = P(blue reported) P(blue cab | blue reported) + P(green reported) P(green cab | green reported)

P(blue cab | blue reported) = ( 0.8 - P(green reported) P(green cab | green reported) ) / P(blue reported)

The answer cannot be calculated without more information.

Essentially the problem is worded incorrectly.

>>10450237
>Blue taxi, correct witness = 15 x .8 = 12
>Blue taxi, wrong witness = 15 x .2 = 3
Incorrect. 0.8 is not the probability of a witness reporting blue given the cab is blue.

>>10450221
>this blue collar cope

>>10450245
15 of the taxis are blue.
If he's right 80% of the time, that's 12 taxis he was right on.

85 of the taxis are green.
If he's wrong 20% of the time, that's 17 taxis he was wrong on.

The other two options are not possible.

so Blue Taxis / Total Possible Taxis is the answer

>>10450268
>If he's right 80% of the time, that's 12 taxis he was right on.
That implies that 12 is the number of taxis he reported on, not the number of taxis in the city...

>>10449989
0.8*0.15 = the chance the witness is correct
0.2*0.85 = the chance the witness is incorrect

0.8*0.15 / (0.8*0.15+0.2*0.85) = the chance the car is blue

>>10450268
>15 of the taxis are blue.
>If he's right 80% of the time, that's 12 taxis he was right on.
That would only be true if 15 is the number of taxis he reported on, not the number of taxis in the city...

>>10450274
>0.8*0.15 = the chance the witness is correct
0.15 is the chance of a blue taxi and 0.8 is the chance of a correct report given he made a report. Their product is meaningless.

>>10450277
idk im just trying to understand this thing

>>10450038
>>10450004
>>10450008
the actual number of blue and green taxis is significant. consider the following my brainlet brethren.
suppose you lived in a city with a million taxis in it. now say 999,999 are green and 1 is blue.

then if someone says they saw a blue taxi and they an 80% chance of being correct, there's 999,999 green taxis for them to fuck up and misidentify as blue

>>10450242
This seems to be the correct definition of the event "witness is correct"

>>10450282
>then if someone says they saw a blue taxi and they an 80% chance of being correct, there's 999,999 green taxis for them to fuck up and misidentify as blue
Nope, because here 80% is the chance of a report being correct given they made a report, not the chance of reporting the car is blue given the car is blue. So there is no connection between 80% and the proportion of cars that would give us the answer.

>>10450242
>>10450287
So the correct answer is "insufficient information"?

>>10450293
Yes, unless by "such statements" they are specifically referring to the statement that the car is blue. In that case the answer is 80%.

>>10450295
>insufficient information or 80%

How to beat 90% of the questions on /sci/:
Learn conditional probability

>>10450237
You should never be allowed to give a TED talk.

Now even uni lecturer's cannot pose Bayesian problems correctly. No wonder students turn out as they do.

it all depends on your interpretation of the line

>witnesses are correct 80% of the time when making such statements

That can either mean that
>witnesses are correct 80% of the time they report a blue taxi
>witnesses are correct 80% of the time they report the colour of a taxi

>>10450295 has it right

>>10449989
I couldn't give less of a shit about probability problems. I could never develop an intuition for them anyway

>>10450275
You’re not seeing the bigger picture.

>>10450447
>>10450295
samefag

Fantastic problem to show modern probability theory is fucking retarded. Maybe that is a bit harsh. Let me rephrase. Probability theory is incredibly limited in its scope and application.

>>10450735
On the contrary, probability theory is one of the most useful ideas humanity has developed. Shame most people are too stupid to get how it works.

>>10449989
50%.
It's either blue or green.

>>10449989
80%

Its beyond me how people in this thread and on /sci/ are so stupid.

Guys.
There is a discrepancy here.
We know there is at LEAST one blue taxi involved.
Re-read OPs opening statement statement and then their question.

>>10450974
>Its beyond me
u got dat rite

>>10450985
It could be all blue taxis! It doesn't specify colors, it could be all taxis. The answer is 100 percent, round up all taxi drivers and have them shot, quick!

>>10449989

12/29. Bayes' Theorem.

>>10450150
This doesn’t take into account the probability of the witness being colour blind

>>10450293
no, the correct answer is to punch whoever worded the question in the face.

>>10449989

Around 41%. I'm surprised by the result.

>>10449989
>witnesses are correct 80% of the time
>what's his chance of being correct
Either fix the phrasing or fuck off.

>>10450126
I agree

>>10451051
Actually, it does, that measure is stored in the witness accuracy probability.

>>10451111

To clarify, just code this up and you'll see that >>10450237 at least gets the correct result.

Run many experiments where you randomly assign the taxi for the crime and the witness's accuracy in describing the color of the taxi (with the probabilities given), and keep track of how many times the witness says blue, and how many times it's actually blue. You'll get this person's answer.

>Implying /sci/ is even capable of the most basic coding.

>>10450378
See >>10450242

>>10450465

>>10451010
>>10451111
>>10451210
Wrong. See >>10450242

It's just hard to understand what the intermediate steps mean in the solution to this problem. They have to mean something.

>>10449989
the chance is 100%.
the police are just sloppy and using "witnesses" as an excuse.

Crime is a spook

>>10451238
yeah no, it's bs

>>10451464
Great argument.

>>10449989
Let B, G represent the events "a blue taxi was involved in the crime", "... green ..."
Let W represent the event "the witness says that the taxi is blue"

P(W|B) = 0.8 # witness gives correct statement 80% of the time
P(B) = 0.15 # base rate of 15% blue taxis
P(W|G) = 0.2 # witness gives incorrect statement 20% of the time
P(G) = 0.85 # base rate of 85% green taxis
P(W) = P(W|B)*P(B) + P(W|G)*P(G) = (0.8)*(0.15) + (0.2)*(0.85) = 0.29 # law of total probability

P(B|W) = P(W|B)*P(B)/P(W) = (0.8)*(0.15)/(0.29) ~= 0.4138 # Bayes' Rule

>>10450974
Yup, even my girlfriend figured it out on her own and she doesn't exist

Let B, G represent the events "a blue taxi was involved in the crime", "... green ..."
Let W represent the event "the witness says that the taxi is blue"

Assuming "witnesses are correct 80% of the time when making such statements" means that witnesses report the colors they see correctly 80% of the time:

P(W|B) = 0.8 # witness reports the color they saw correctly 80% of the time
P(B) = 0.15 # base rate of 15% blue taxis
P(W|G) = 0.2 # witness reports the color they saw incorrectly 20% of the time
P(G) = 0.85 # base rate of 85% green taxis
P(W) = P(W|B)*P(B) + P(W|G)*P(G) = (0.8)*(0.15) + (0.2)*(0.85) = 0.29 # law of total probability

P(B|W) = P(W|B)*P(B)/P(W) = (0.8)*(0.15)/(0.29) ~= 0.4138 # Bayes' Rule

Assuming "witnesses are correct 80% of the time when making such statements" means that color reports from witnesses turn out to ultimately be correct 80% of the time (which makes the question stupid):

P(B|W) = 0.8 # color report from witness is correct 80% of the time

>>10450293
It's insufficient information ONLY in the sense that people need to become informed on the implications of false positives.
There is nothing ambiguous about the question or answer.

>>10450287
>80% is the chance of a report being correct given they made a report, not the chance of reporting the car is blue given the car is blue.
Actually it's the second part AND another part that you forgot.
The "80% correct" is:
Chance of reporting the car is blue given the car is blue AND the chance of reporting the car is green given the car is green.

If there are 20 billion green taxis and 1 blue taxi, and your friend comes and says I JUST SAW A BLUE TAXI and his statements are 99% correct, you would still tell him to look again, wouldn't you? Because the chance that the sun was in his eye and he got the color wrong is higher than the miniscule chance that he actually came across a blue taxi. Think about it.

>>10449989
Okay, I think these are the minimal assumptions necessary:

Let B, G represent the events "a blue taxi was involved in the crime", "... green ..."
Let W represent the event "the witness says that the taxi is blue"

Assuming "witnesses are correct 80% of the time when making such statements" means that witnesses report the colors they see correctly 80% of the time. Also assuming that witnesses will never misreport a color that is not present at all in Carborough:

P(W|B) = 0.8 # witness reports the color they saw correctly 80% of the time
P(B) = 0.15 # base rate of 15% blue taxis
P(W|G) = 0.2 # witness reports the color they saw incorrectly 20% of the time
P(G) = 0.85 # base rate of 85% green taxis
P(W) = P(W|B)*P(B) + P(W|G)*P(G) = (0.8)*(0.15) + (0.2)*(0.85) = 0.29 # law of total probability

P(B|W) = P(W|B)*P(B)/P(W) = (0.8)*(0.15)/(0.29) ~= 0.4138 # Bayes' Rule

Assuming "witnesses are correct 80% of the time when making such statements" means that color reports from witnesses turn out to ultimately be correct 80% of the time (which makes the question stupid):

P(B|W) = 0.8 # color report from witness is correct 80% of the time

>>10451579
>>10450242
>>10450116
>>10450124
>>10450287
>muh ambiguous wording
>because here 80% is the chance of a report being correct given they made a report
This would lead to idiotic contradictions and could only be interpreted this way by a complete brainlet

Change the problem a bit: suppose there are NO blue taxis in the city. Not even one.

100% of taxis are green, 0% of taxis are blue.
Now, witness says to you "The taxi was blue." Witnesses are correct 80% of the time when making such statements.
What's the chance that the taxi is blue?
Still not enough information? Still 80%?

>>10451476
go back to >>>/x/

>>10451513
>P(W|B) = 0.8 # witness gives correct statement 80% of the time
P(W|B) is the chance that a witness reports a blue car when the car is blue. The question on the other hand says that the witness will be correct 80% of the time they make such a statement, not 80% of the time the car is blue.

>>10451579
>Assuming "witnesses are correct 80% of the time when making such statements" means that witnesses report the colors they see correctly 80% of the time
That would mean 0.8 = 0.15*P(W|B)+0.85*P(~W|G)

P(W|B) = ( 0.8 - 0.85*P(~W|G) ) / 0.15

Nowhere does the question say that witnesses are correct 80% of the time the car is blue.

>>10451594
>The "80% correct" is:
>Chance of reporting the car is blue given the car is blue AND the chance of reporting the car is green given the car is green.
That is a better interpretation than the chance of reporting the car is blue given the car is blue, but it's still not a good interpretation since the question specifically says "when they make such a statement." So the condition is making such a statement, not the car being a particular color. Your interpretation assumes that someone MUST make a report when they see a blue or a green car.

Also, your new interpretation does not allow you to solve the question, so yes, it's insufficient information.

>>10451629
>This would lead to idiotic contradictions and could only be interpreted this way by a complete brainlet
What contradictions?

>>10451632
>>>/b/

>>10451610
See >>10451659 and >>10451664

>>10449989
Assume the average /sci/ poster has 80% chance of being correct when answering to probability related OP questions. Given that one such poster responded to this very questions with 80% what's the probability that's the correct answer to the OP?

>>10451686
100% since that is the correct answer.

>>10451672
Maybe read the rest of the post?
Can you only read text if it's in an image?

OK, see pic related.
What is your answer, and why?

>>10451727
>Maybe read the rest of the post?
I did, no contradictions with the question in the OP were presented.

The answer to your question is 0, but no contradiction is presented since the 80% correct report rate simply means that witnesses have an 80% chance of reporting a green car.

>>10451741
>The answer to your question is 0
How?
The witnesses are correct 80% of the time. If they say the taxi is blue, then it's blue 4 out of 5 times.

>>10451751
>How?
Because there are no blue cars.

>The witnesses are correct 80% of the time.
Yes, because they report a green car 80% of the time and reporting a green car is always correct since all cars are green.

>If they say the taxi is blue, then it's blue 4 out of 5 times.
No, the question does not say that they are correct 80% of the time they report a blue car, it says they are correct 80% of the time they make a report. They can also report a green car correctly.

>>10451761
>Yes, because they report a green car 80% of the time and reporting a green car is always correct since all cars are green.
The image clearly states that the witness reported a BLUE car. Try again.

>>10451761
>Because there are no blue cars.
So the actual number of taxis matters after all, then?

>>10451764
>The image clearly states that the witness reported a BLUE car. Try again.
Yes, they had a 20% chance of reporting a non-green car and they did. What is your point?

>>10451766
Only if all taxis are blue or none are blue. Which is not the case in the OP. So what is your argument?

>>10449989
59%

>>10449989
0%. Carborough is a mine and thus would have no taxis. They probably hit some bad gas down in the mine and the "witness" is hallucinating.

>>10451772
So you agree that if you know, a priori, that the witness is wrong, you can completely discount his testimony, correct?

>>10451768
Earlier (>>10451670), you said
>the condition is making such a statement, not the car being a particular color.
This means that given the witness makes a statement, there is an 80% chance that it's correct.
But now you're saying that given the car is a certain color, there is an 80% chance he names the right color.
So which is it?

>>10451790
>So you agree that if you know, a priori, that the witness is wrong, you can completely discount his testimony, correct?
Of course.

>This means that given the witness makes a statement, there is an 80% chance that it's correct.
>But now you're saying that given the car is a certain color, there is an 80% chance he names the right color.
No, let's review the math:

0.8 = P(blue reported) P(blue cab | blue reported) + P(green reported) P(green cab | green reported)

If all cars are green, we know any blue report is never correct and any green report is always correct:

0.8 = P(blue reported)*0 + P(green reported)*1

0.8 = P(green reported)

>>10451811
Whoever argues with this is either a clueless brainlet or a coping brainlet

>>10451811
So in this scenario, he reports blue 20% of the time, because the cab is always green?
In other words, the chance of a blue report depends on what percentage of cabs are green?

>>10451986
Yes, but only in this scenario. If all the cabs were blue then witnesses would report blue 80% of the time. This is only possible to determine in the edge cases.

>83%
>80% chance he saw correctly, 15% of remaining 20% chance he got lucky. Thus 80+20*0.15=83%

>>10450282
Youre an idiot.

>>10451210
Poster of >>10450237 here. I was going to code this up but then realized being able to write equations like this makes coding it an unnecessary effort.
Everyone's problem here is the ambiguity in "making such statements."
They cant extrapolate from simple social cues as a result of their autism.

>>10452000
>If all the cabs were blue then witnesses would report blue 80% of the time
Hmm, that's interesting.
I wonder what happens in the middle. i.e. Suppose 99% of the cabs were blue, what percentage would be reported blue, and what percentage of those would be correct?
Feels like there ought to be some kind of a function to describe it..

>>10452491
All percentages in decimal format (15% = 0.15)

B = percent of Blue taxis
G = percent of Green taxis

C = percent Correct
W = percent Wrong

(B * C)
/
(C * (B - G) + G)

>>10452357
>Everyone's problem here is the ambiguity in "making such statements."
no ambiguity at all, autism or not.
see >>10451727 where it's known a priori that the chance of a blue taxi is 0%.
accurate application of bayes theorem still yields the correct answer of 0%.
meanwhile, the 4chan brainlet logic yields a contradiction: the witness's statement is presupposed to be correct 80% of the time in a situation where it can never be correct.

to address this, the brainlet quickly carves out an exception where a priori knowledge CAN be admitted; but, only in edge cases!

It's -1/12, that is the only correct answer

>>10452491
It could be any percentage, there is no way to determine it with the information given.

>>10452828
>the witness's statement is presupposed to be correct 80% of the time in a situation where it can never be correct.
No, as I already explained, a witness can report any color of car. If they report green then they are correct. So there is no contradiction.

>to address this, the brainlet quickly carves out an exception where a priori knowledge CAN be admitted; but, only in edge cases!
A priori knowledge exists in all cases since we know the percentage of green and blue cars. I don't think you understand the terms you're using. The only thing interesting about the edge cases is that terms cancel out and conditions don't matter.

>>10449989

0%

Her story fell apart when it was revealed that she is blind.

She was the killer and made up the story about a taxi.

20 years of watching TV detective shows has finally paid off.

>>10449989
>make up 15% of the taxis
>involved in 50% of the crimes

am i the only one seeing this? the answer is black people

>>10451240
>i can use mspaint

>>10453211
It's a simple problem that answers itself but /sci/ is so inclined to be right by proving others wrong that they'll jump through hoops. I would use a question like this as a professor to demonstrate that common sense is still valuable in STEM

>lol if u didnt study probability like le me ur a fagit breinlet idiot poopface lol!!!!

This type of "Let's see if /sci/ is smart" threads belong to /trash/.
And before you ask, no, I don't know the solution to that shit fucking problem nor do I care enough about it to start to actually try to resolve it.

>>10453351
it's 80%

if OP was a detective hed be a shit detective

>>10450237
Great explanation. You start out by calculating probabilities and apply them to relative risk.

>>10453211
>If they report green then they are correct.
And if they report other than green, then they're incorrect, since all taxis are green.
And it's given they will report incorrectly sometimes, since it's stated that they are correct only 80% of the time.
Then the chance that the taxi is green is 100%, but the witness only says it's green 80% of the time.
Thus, the witness' accuracy rate is not necessarily the same as the chance that the taxi is green, and to assert otherwise is wrong.

>>10453263
Professors already use problems like this as an example of how common sense is a poor substitute for careful, examined reasoning.

>>10453439
>And if they report other than green, then they're incorrect, since all taxis are green.
Yes, that's what I said here >>10451811

>Thus, the witness' accuracy rate is not necessarily the same as the chance that the taxi is green, and to assert otherwise is wrong.
Where did I assert that? I said the chance of the witness reporting a green taxi is the same as the accuracy rate, not the chance of a green taxi.

>>10453255
>I can't handle multiple people disagreeing with me

>>10453392
His explanation is wrong from the very first calculation.

>>10449989
teh chance is 0 because the witness is stupidd

Actually it's [math]\frac{80\% * 15\%}{20\% * 85\% + 80\% * 15\%}[/math] which is approximately 41.3% if my arithmetic is correct.

>>10450040
+1

>>10450056
Bayes' theorem.

>>10450121
Natural language is fuzzy. You need to discern that it means P(the witness reported a blue taxi | the taxi is blue) = 0.8 via context, because the question would be completely pointless otherwise.

>>10450126
You calculated the weighted average chance that the witness would report blue, not the chance that the car would actually be blue given that they reported blue.

To get that you need to use bayes' theorem.
[eqn]P(A|B) = \frac{P(A)*P(B|A)}{P(B)}[/eqn]
(what you calculated goes to the bottom)

>>10450215
Yeah, but they obviously meant that for all x since otherwise the problem would be unsolvable.

>>10450221
Psychology majors study this anon to learn how people rationalize being stupid so they can feel good with themselves.

>>10454255
>Where did I assert that?
You conditionally asserted it here >>10450242
>If by "witness are correct 80% of the time when making such statements" they mean the witness is correct 80% of the time they say they saw a blue taxi then the answer is 80% and the other information given is unnecessary.

>>10454271
If you don't understand the explanation then you don't understand the problem. If the witness is asked 100 times, he will correctly say blue 12 times, incorrectly say blue 3 times, correctly say green 68 times, incorrectly say green 17 times. Correctness depends on what the actual car was in the scenarios.

>>10454302
>41.3%
The witness is still stupid.

>>10454322
If this question was on a test, sure. But there is no need to interpret it generously here. I find it much more amusing to discuss it as written.

>>10454387
That says that *if* 80% is the proportion of times a person reporting blue is correct then the chance that the taxi is blue is 80%. How is this false?

>>10454870
that's not what that says though

>>10454458
>If you don't understand the explanation then you don't understand the problem.
I understand both, and his calculation is wrong. Multiplying the number of blue taxis by 0.8 to get the number of correctly reported taxis implies that 0.8 is the chance of a taxi being reported blue given its blue. The question does not say that. It says 80% is the chance of the witness being correct given they made such a statement. Do you understand the difference?

>If the witness is asked 100 times, he will correctly say blue 12 times, incorrectly say blue 3 times, correctly say green 68 times, incorrectly say green 17 times.
This can't be concluded from the information given by the problem.

>>10454883
It is. How are they different?

>If by "witness are correct 80% of the time when making such statements" they mean the witness is correct 80% of the time they say they saw a blue taxi then the answer is 80%

>*if* 80% is the proportion of times a person reporting blue is correct then the chance that the taxi is blue is 80%.

>>10451527
kek

>>10454897
And if we knew ahead of time that the chance that the taxi is blue is 0%, then 80% couldn't possibly be the proportion of times that the person reporting blue is correct.
Thus that could not have been their meaning. There is no "if" here. The meaning is clear.

>>10454958
>And if we knew ahead of time that the chance that the taxi is blue is 0%, then 80% couldn't possibly be the proportion of times that the person reporting blue is correct.
>Thus that could not have been their meaning.
Changing the question so that it contradicts itself has no bearing on the meaning of the original question.

The meaning is clearly not 0.8 = P(blue reported | blue taxi) since the proportion of witnesses that are correct when making such statements is the opposite of that.

>>10455070
>Changing the question so that it contradicts itself has no bearing on the meaning of the original question.
Yes. Precisely. Misinterpreting the statement about the witness accuracy rate creates a contradiction that makes the original question nonsensical.
We've been trying to tell you that this whole time. Glad you finally caught up.

>>10455672
>Yes. Precisely. Misinterpreting the statement about the witness accuracy rate creates a contradiction that makes the original question nonsensical.
What contradiction? The only contradiction you've shown is when you change the proportion of taxis to all green.

>>10450287
What about the 20% chance that the witness is wrong, in the case of the witness seeing a yellow taxi but claiming it was blue?

>>10450282
Yeah but if there's 1 blue taxi in the city, it's pretty hard to miss. It would almost be a novelty. Now you're starting to get into how new is the person to the city and how likely are they to know about the blue anomoly.

>>10455777
Based trips, the novelty of the stimuli is important

>>10455762
What about it?

>>10449989
80% of 15% which is 12%.

12%

>>10451119
There is no contradiction in the phrasing. The question is asking for the probability of the taxi being blue. This is already answered by the premise: 15%.
The hang-up some participants in the thread seem to be having is with language and the dependency of the events. The two events are independent in the sense that the color of the taxi (15% blue 85% green) has nothing to do with the witness being correct (80%).

The two statistics can be shown to "exist" at the same time as follows
Case 1: Blue Taxi-Correct Answer = 15*80=12%
Case 2: Blue Taxi-Wrong Answer = 15*20=3%
Case 3: Green Taxi-Correct Answer = 85*80 = 68%
Case 4: Green Taxi - Wrong Answer = 85*20 = 17%

Summing in regards to either the correct of the answer or the color of the taxi generates both of the probabilities given.

>>10455987
>There is no contradiction in the phrasing. The question is asking for the probability of the taxi being blue. This is already answered by the premise: 15%.
Incorrect. The probability of this particular taxi being blue is the probability of a taxi being blue given a witness reported a blue taxi.

> The two events are independent in the sense that the color of the taxi (15% blue 85% green) has nothing to do with the witness being correct (80%).
How do you know that? Don't just make things up if you don't know how probability works.

Also your calculations don't really make any sense. Is 15% the chance of reporting a blue taxi and 80% the chance of a taxi being blue given it was reported blue? No.

>>10454850
That's reasonable as well, it's just that if you actually want to solve the problem that was attempted to be presented, then you should interpret it as such. I agree with you that it might be more fun to analyze it otherwise.

>>10456428
That is in no way what the problem is asking. The question asks what the probability of a blue taxi being involved is. If the witness didnt exist and the event occurred, the probability would be 15%. The witness guess doesnt impact the chance the taxi is blue. I dont see how one could interpret the question any other way. Believing it means what you indicated would require a very weird reading of the English.

As for the next part, an anon above already clarified that easily. If the problem said police know 100% of cars of green, then how could the accuracy of witness testimony have anything to do with car color or the question's answer.

And in regards to my calculations, I dont know what isnt clear to you. 15% is the chance any taxi seen at any time is blue and 80% is the chance a witness seeing said taxi will report correctly.

>>10449989
>making such statements
Here's what it means for you brainlets:

If a blue taxi were really involved, the witness might report blue (with 80% probability) or green (with 20% probability). If a green taxi were really involved, the witness might report blue (with 20% probability) or green (with 80% probability).

>>10454887
The only difference on this website is blue and green switched, 85 blue 15 green, so I changed pic related to be relevant to OP's problem.

https://plus.maths.org/content/solution-taxi-problem

Check the website to see your error. It's okay to admit you were wrong on here, you're not gonna lose anything.

>>10455867
How did you reach that conclusion?

>>10456820
>That is in no way what the problem is asking. The question asks what the probability of a blue taxi being involved is. If the witness didnt exist and the event occurred, the probability would be 15%. The witness guess doesnt impact the chance the taxi is blue.
Of course it does. The question is asking what is the probability a blue taxi was involved in this particular crime, not the probability in general. Any information we have about this crime can effect that probability. I dont see how one could interpret the question any other way. Believing it means what you indicated would require a very weird reading of the English.

>As for the next part, an anon above already clarified that easily. If the problem said police know 100% of cars of green, then how could the accuracy of witness testimony have anything to do with car color or the question's answer.
If the problem was different it would be different. This has no bearing on the question as it's written.

>15% is the chance any taxi seen at any time is blue
If by "seeing" you mean that a blue taxi is actually there, then yes. But that's different than the chance of *reporting* a blue taxi.

>and 80% is the chance a witness seeing said taxi will report correctly.
No, the question says that 80% is the chance of a witness making such a statement being correct. Now there are two ways to interpret this:

1. The probability that the taxi is blue given the witness reported a blue taxi

2. The probability that the taxi is x given the witness reported x.

If the meaning is 1 then the answer to the question is trivially 80%. If the meaning is 2 then the question can't be answered because we need to know the probability of a blue report, the probability of a green report, and the probability of a taxi being green given it was reported as green.

>>10456844
>If a blue taxi were really involved, the witness might report blue (with 80% probability) or green (with 20% probability).
No, 80% is the probability of the report being correct given such a report is made, not the probability that the report is correct given the car is blue. It specifically says "when such a statement is made" not, when the car is blue.

>>10456891
The website is wrong for the same reason. Please explain to me how "when such statements are made" = "when the car is blue." They are entirely different, yet most people reading the problem will simply gloss over this because they intuit that this is a conditional probability question that can be solved using Bayes' theorem. Wording your problem correctly is important.

>>10456769
If you actually want to solve the problem then interpret "when such statements are made" as "when a witness reports a blue car." This immediately gives you the answer 80%.

I know according to Baye's theorem it's 41% but what is the proportion of green and blue taxis in the studies that establish the witness reliability? Is it also 15% and 85%? Is it 50% 50%? I think that's the element that makes everyone so confused.

>People arguing about the fact that the question replies itself and that if such studies exist and someone read them then he sould not pose such stupid question.
Well, actually the car is both green AND blue untill the witness sees it and there is no way to determine how it will be after...

>>10449989
0% taxi color is a social construct

>>10449989
80%
The second point is tangential information

>>10457106
I'm sensing some strong cognitive dissonance from your side. "There's no way I'm wrong, THE WEBSITE must be wrong."
Which is more likely, you are wrong or the website is wrong?

>>10457087

>>10458178
I'm sensing that you have no argument for how you can interpret "when making such statements" as "when the taxi is blue." The website is clearly wrong.

>>10458185
The witness has a 1% chance of reporting a blue taxi and the chance that the taxi is blue is 100%. No contradiction. Also, changing the problem to create a contradiction has no bearing on the original problem. Some questions can't be answered and some questions don't make sense, get over it.

>>10455867
The only high IQ post in this thread

>>10458185
Still 1%: maybe all taxis are blue but he might have seen a normal car and not a taxi; maybe in that city taxis are very similar to cars.
Come on /sci/ brainlets, learn how to read and understand a sentence!
>>10458178
Plenty of websites out there saying the earth is flat...

>>10457059
I stuck a carrot in my ass and farted. The carrot flew for 12 inches.

>>10449989
If the taxi is blue then it is more likely that the taxi was never green to begin with. The question then describes a momentum based approach to arriving at a situation in which a concrete setting is now treated as a position of advancement. This means that the only available place for a person to use their "color" makes them available to only the useful parts of the problem. That sets them ahead and makes the chance that another continue 80% of the people will conclude that this car was indeed blue. The setting will describe for a car that was indeed not blue and that will change the scenario to include that there may be a car with color green. But unless the setting describes a car with the same setting as the one another setting may describe as green is in existence, meaning we have them set to equal each other by a manner of describing to being blue or green, we have the manageable pieces to arrive at the conclusion that the car is only blue 80% of the time because the green car's "opportunity" to be less than 80% of the time excluded is the opportunity that while 15% of the cars in Carborough are blue, the situation doesn't change just because the only other option for finding a value is the converse. This is invalid but it is not a thinker's choice. It's dialectic.

>>10450282
No wonder you fuckers want to become scientists, absolutely no lateral thinking abilities whatsoever

>>10459150
Tell me not that this means it's like saying it's undefined.

>>10449989
>80
reason why that shit is red cause it doesn't matter this was an example in a lecture not a hw problem

>>10459157
Could be a null hypothesis but I"m suggesting no corollary may interact within the boundary of the mind and all exaction is being funneled out of thought into the mind as if the thought came from the mind. It's ridiculous banter and all holders of that belief should be questioned, hung and shot for the sake of clarifying the father, the son and the mother that we don't take kindly to terrorists, bigot or totalitarian regimes.

>>10459146
jk, I pulled it out of my ass

>>10449989
Think of it as testing for smoking pot. If you KNOW (emphasis added) only 1 in 1000 people statistically smoke pot from super expensive and accurate testing and you have a cheap test that's 99% accurate you'll get 10 false positives if you test 1000 people and the one guy who smokes pot has a 99% chance of testing positive on top of that.

So odds of a positive test being correct is .99 out of 10.01 or something like that and that should be pretty easy to mentally visualize. It's way harder to mentally visualize if the fractions are close together like 85% and 80% and seems completely unintuitive.

>>10449989
https://en.wikipedia.org/wiki/Representativeness_heuristic

>>10459277
To be fair I thought it was 80%. I feel pretty stupid now that I read the explanation.

>>10449989

(possibility of PERSON seeing BLUE car) = .8
(possibility of a BLUE car) = .15
(possibility of seeing a car) = ??? lets assume 100% = 1

(.8)(.15) / 1 = .12 or 12% chance

>>10459351
it's "possibility of PERSON reporting BLUE correctly" ya dingus

>>10459360
Yeah whatever, point is P and B are tied together somehow, maybe by your mum, I don't give a fuck, P|B.

>>10459277
>>10459280
>The court tested the reliability of the witness under the same circumstances that existed on the night of the accident and concluded that the witness correctly identified each one of the two colors 80% of the time and failed 20% of the time.
This is a different problem. Instead of saying that the witness is correct 80% of the time they make such a statement, it says the witness is correct 80% of the time the taxi is blue and 80% of the time the taxi is green.

>>10452007
Daily reminder that this is the only correct response in the entire thread

P(saying bue car and cae is blue) = P(saying car is blue) * P(the car is blue | saying car is blue) = 1*0.8 = 0.8

>>10459386

>>10459497
nope, 41.38% it is

>>10459497
>>10459518
Nope 80% is.

>>10459522
[monte carlo simulation needed]

The witness can be either correct or incorrect.
The probability of him being correct is 80%.
The probability of him being incorrect is 20%.
He said the car was blue, if he's wrong the car is green.
The probability of the car being blue is 80%.

>>10459518
41.38%

>>10459540
No need, the problem states that witnesses are correct 80% of the time when making statements that a taxi is blue. Since the witness reported a blue taxi the chance he's correct and the taxi is blue is 80%.

>>10459583
>no proof needed
the quintessential sign of the religious nut
faith, revelation etc.

https://youtu.be/VxGMqKCcN6A?t=11m

>>10459607
>no proof needed
I just gave you proof, moron. A literal proof.

>>10459579
>P(blue and reportedBlue) = 80%
Completely wrong.

>>10459914
no wonder you don't have a clue

>>10459914
P(color is same as reportedColor)
would be a better name, but mathematically it is correct.

>>10459934
>>10459952
80% is P(blue | reported blue)

Or it could be P(x | reported x), but that means their is insufficient information to answer the question.

Also, if 80% is P(blue and retorted blue) then it must be less than or equal to P(blue) and multiplying it by P(blue) is meaningless.

>>10459971
so-o...
which number(s) in the n=1000 case is wrong?
what would your numbers be?

150? 120? 30?
850? 170? 680?
1000? 290? 710?

>>10459579
why not make n = 100?
It's more intuitive if divided by a factor of 10.

>>10459579
This is ridiculous, The proportion of blue cars is irrelevant to the problem.

A witness sees a crime involving a Monster Truck in Carborough. It is known that from previous research that witnesses are correct 80% of the time when making such statements.

Police also know that 99.99999% of the cars in Carborough are not Monster Trucks, the other 0.00001% being Monster Trucks.

What is the probability that a Monster Truck was involved in the crime?

80%, because the witness testimony is 80% reliable. The Frequency of monster trucks appearing in the vehicle population is irrelevant to the Probability that the witness is correct, insofar as this problem is stated. To think otherwise is just to deny rare events because they are rarer than alternatives.

>>10459989
mspaint is your friend, go wild

>>10460001
>>10459982

>>10454322
Think very carefully about what you just did here. The natural interpretation is P(B|wB) = 0.8, trivializing the question. Which it deserves because it's a stupid question.
You are purposefully "discerning" the exact opposite formulation, P(wB|B) = 0.8 because *you* feel the question needs to have a point. You're adding this condition to a problem that does not deserve it. Trivial problems exist. You're adding meaning where none exists and that's why this thread is stupid.

>>10449989
2

>>10459491
>This is a different problem.
Get your head out of your ass! It's literally the same problem, but you've invested so much time and effort into believing that 80% is the correct answer, that you don't want to accept what the evidence actually points to. The taxi cab problem is from Tversky and Kahneman meant to illustrate our faulty intuitions when it comes to probabilities. What else would be the point of solving this problem? "Witnesses are correct 80% of the time. Student: Oh the answer is right there, problem complete!" Do you see how that would teach the student absolutely nothing?

Look up cognitive dissonance.

>>10460004
Your argument is a non-sequitur. If n=1000, the correct formulation is: N(witness is correct) = 800, N(witness is incorrect) = 200. The other information is irrelevant.

>>10460018
You can apply what you said directly to yourself, you're convinced it's not a badly worded problem that, as written, is as trivial as it looks. You could just as easily say it's a trick question, to give overachievers something to waste time overthinking when the answer is trivial.

>>10460001

>>10460028
you are ignoring how the misreported greens are polluting the blue's data

>>10459982
Only 150, 180, and 1000 are correct. But we don't need any of these numbers to solve the problem.

>>10460044
180 isn't in the list
kek

>>10460040
Now that the numbers are extreme, you should be able to see why this is nonsense. So, here's a hint: define very clearly what event "monster" denotes.

>>10460018
>Get your head out of your ass! It's literally the same problem
It's literally the opposite problem. Instead of saying that the witness is correct 80% of the time they report a blue taxi, it says the witness is correct 80% of the time the taxi is blue.

You clearly have no idea what you're talking about since you have repeatedly failed to respond to the argument and instead post websites that you believe have the right answer or believe to be discussing the same problem. Yet when confronted with an explanation of how that belief is wrong, instead of validating that belief, you post "cognitive dissonance." It's pretty amusing.

>The taxi cab problem is from Tversky and Kahneman meant to illustrate our faulty intuitions when it comes to probabilities.
This isn't the same problem, but it has served the same purpose since it's shown that instead of reading and understanding what the probabilities are, you operate on autopilot and simply assume two similar questions are the same question.

>Look up cognitive dissonance.
Please tell me what my contradicting beliefs are.

>>10460034
So, in essence, this whole thread is about:
Is this a trick question?
A. Yes, the answer is 80%
B. No, the answer is 41.38%

Depends on the professor you get in that case.
Personally, I would not make this a trick question as there's a much better lesson to learn about our erring in probability from the taxi cab problem than to be like "Ha! Gotcha! The answer was right there!"

>>10460040
Although at first glance, you might think this is a ridiculous conclusion, this makes sense.
Think of bigfoot sightings. Let's pretend there is at least one bigfoot, however there are hundreds of sightings all around the US.
So the probability of (not bigfoot and reported bigfoot) is going to be astronomically high.

>>10460041
"misreported greens" is an invention of your own interpretation. The problem states the witness is correct 80% of the time independent of situation. So, there's an 80% chance the car is a blue taxi. It's a tautology, a trivial question. You are reading too much into it.

>>10460040
This fails for the same reason. 0.8 is the probability that a report of a certain type will be correct, not a certain type will be reported correctly. Do you understand the difference?

>>10460046
850

>>10460059
the prompt did it already,
- witnesses report the color correctly 80% of the time
- blue taxis are 15% of the total ---> monsters are 0.00001% of the total
which number in >>10460040
is not in tune with those two statements?

>>10460062
>it says the witness is correct 80% of the time the taxi is blue.
Where does it say that?

>but it has served the same purpose
not at all

>what my contradicting beliefs are
You thinking 80% is the answer
Wikipedia article showing 41.38% is the answer

So you have to put an ad hoc: "It's not the same problem!"

>>10460079
really? n=1000
so how many green taxis do you think there are?

>>10460064
Yes, pretty much. Based on the wording presented it's a trick question but some others may read the alternative into it. That situation is inverted with a small change of wording just like every other problem of this kind that gets posted to /sci/. The only way to win is to win the metagame, and not the game itself, by realizing this.

>>10460080
That is not what I asked, I said define the event that "monster" represents explicitly. You're getting ahead of yourself and that's the problem.

Let’s put it this way. There’s an 80% of the testimony being correct.

There ya fuckin go.
You could choose to do a bunch of other probably mumbo jumbo, but baseline, the witness gives an 80% chance of blue.

>>10460064
It's just as important to teach people not to assume they know how to solve a problem without thinking about it based on its similarity to other problems as it is to teach people conditional probability. If you don't know conditional probability then the latter is better. If you do know conditional probability then the former is better.

>>10460059
See >>10460071

>>10460084
850

>>10460086
the wording is fine
the answer is 41.38%

the 80% supporters seem to think the prompt is stating the accuracy is 80% only when they are reporting on blue cars
The text doesn't say in any way or form that the same 80% doesn't apply for green cars as well

>>10460101
>isn't 850
>is 850
k

>>10460099
The problem tells us what the chance of a Bigfoot report being correct is. You can't assume it's low from the information given.

>>10460108
>isn't 850
I never said this.

>>10460091
idk what you're talking about.
I'm not going to discuss anything that isn't joined at the hip to the prompt.
Anything else is just a waste of time.

>>10460104
If 80% = P(blue|blue reported) then the probability for green cars is irrelevant since this immediately gives us the answer.

If 0.8 = P(blue reported) P(blue | blue reported) + P(green reported) P(green | green reported) then there is insufficient information to find the answer.

Either way, 41.38% is not the answer and the only way to get that is by misinterpreting the problem. Please explain how you got this number.

>>10460115
>>10460079

>>10449989
Judging by the unclear wording I’m starting to think OP is the brainlet. Post the answer so it can be judged.

>>10460134
>>10459579

>>10460138
That's me saying 850 is the correct number instead of 180, genius.

>>10460142
>>10459971

>>10460133
So you're defining the probabilities of events without understanding what an event is and you're surprised and stubborn when you arrive at the wrong conclusion?

Neat.

>>10460157
>hand waving intensifies

>>10460160
Fine then, formulate your argument properly. Here's mine:
Let ~ be the negation symbol, we have...
M : M is the event that criminal was in a monster truck.
R : R is the event that the witness statement of monster truck criminal is correct
~R : the witness statement is incorrect.

P(M) = ?

Total probability:
P(M) = P(M|R)P(R) + P(M|~R)P(~R)
Witness is correct 80% of time, so P(R) = 0.8 and P(~R) = 0.2

P(M|R) is "Monster Truck Criminal" given "witness statement is correct" is a tautology, so P(M|R) = 1

Similarly, P(M|~R) = 0 since "Monster Truck Criminal" and "witness statement incorrect" is a contradiction.

Therefore:
P(M) = (1)(0.8) + (0)(0.2) = 0.8

>>10460190
- witnesses report the color correctly 80% of the time
- blue taxis are 15% of the total

>>10460264
Not an argument. Those are just two facts.

>>10460190
idk how to use Bayes
and since your answer is wrong, neither do you

>>10460271
all my numbers in >>10459579
agree with those facts

>>10460273
Not an argument.

Keep trying.

>>10460275
They don't agree with anything if you can't even define what your terms mean.

>>10460277
>>10459579

>>10460288
>>10460287

>>10460287
>>10460160

>>10460292
I ain't handwaving shit. I showed you my argument from start to finish, you keep waving off requests to do the same.

>>10460291
numbers vs handwaving
numbers win

>>10460295
>I showed you my argument from start to finish
and got a wrong amswer

>>10460295
and got the wrong answer

>>10460299
Your opinion is insufficient proof. You've found 2=1 and you're saying 1=1 is incorrect and treating that as some sort of refutation. It isn't.

>>10451824
But that doesn’t change the fact that you’re a faggot, and I’ve never met a smart faggot.....

>>10460073
20% of the greens get misreported as blue.
this fucks up the reported-as-blue vs was-blue

>>10457122
But that obviously means P(the witness reports a color | that color is correct), and not the opposite.
Otherwise, the problem would be pointless.

Math "logic" answer: bullshit
Common sense answer: 100% blue because a blue taxi is different enough from the norm you can trust the difference would leave an impression on their mind, at least moreso than normal eye witness accuracy.

>>10460306
It should be easy to point out the wrong numbers in >>10459579 then, mr genius
chop chop

>>10460309
Alan Turing

>>10460327
How to destroy a /sci/ fagphob's soul in 2 words.

>>10460326
All of them. What does the odds of simple random selection producing a Blue Taxi / Monster Truck out of the population have to do with accurate reporting of a single case of a crime?

All you're doing is smashing together numbers without any idea of what they mean. All you are doing is picking random cars out of a hat and then flipping a weighted coin to see if you name the color right. P(blue & type is ReportedType) is the frequency that you pick a blue taxi out of the hat and the coin lands on the 80% side. This is totally meaningless because we don't care about the total population, we care about one single member of the population. The proportion of blue and green taxis is irrelevant. The construction of the problem is meaningless, and you got there by not defining your terms and not having any understanding of what the numbers you're playing with mean.

>>10460355
>All of them.
n=1000
15% are blue. You disagree about the 150? Really?

>>10460355
>The proportion of blue and green taxis is irrelevant.
nope, >>10460311

>>10453241
Based.

>>10460376
so was Bin Laden, what do you think al-qaeda means?
fucking retard

>>10460366
Brainlet, n=1000 is irrelevant and something you made up on your own. What do you think that 15% tells you about the situation?

>>10460368
There are no misreportings because we aren't talking about a plurality. The OP specifically refers to "The Crime". Singular. You bringing in other occurrences is your own invention and it pollutes the meaning of the 80% witness reliability figure.

>>10460391
>n=1000 is irrelevant
sure, everything works with 100 or 100000000 too - that's not the point.
But when n=1000 and 15% are blue.
You disagree about the 150? Really?

>>10460391
>There are no misreportings
kek
no wonder you are lost in the woods

>>10460396
Answer the question, what do you think the 15% proportion of blue taxis actually tells you?

>>10460401
There is no statement of green taxis committing crimes. There is no statement of blue taxis committing crimes. There is no statement of the involvement rate of either taxi color in crime. You are asked about one specific taxi and one specific crime given a witness with reliability of 80% for that taxi. The answer is trivial, 80%.

What you're doing is presuming an equal crime rate between blue and green taxis, and then stating the probability that, for all taxi crime, the rate that the taxi involved is both blue and correctly identified as such. So, the probability *you* are reporting is actually the Rate of Blue Taxi crime AND correct identification, given a laundry list of assumptions you were not granted. This also means you're leaving out the proportion of crimes involving blue taxies but are incorrectly reported, so you're not even correct in your own framework.

I tried to lead you to this with baby steps but evidently you're too stupid to understand.

>>10460401
And just so we're unambiguously clear: the question says what is the "probability that the crime involves a blue taxi"? It's not asking you for a rate and is not contingent on correct identification.

You are wrong, give it a rest.

>>10460433
>weird philosophical handwaving
don't know, don't care.

let's talk numbers
n=1000 and 15% are blue.
You disagree about the 150? Really?

>>10460317
It ominously means the opposite of that. The "point" of the problem is either self defeating or to fool brainlets who don't read.

>>10449989
The percentage of blue taxis is irrelevant (well, as long as it's greater than 0% and lesser than 100%). If the witness is correct 80% of the time, and the witness has told us that they saw a blue cab, then there is an 80% chance that they actually saw a blue cab. End of fucking story.

>>10460465
>>10460311

>>10460474
"I tried to lead you to this with baby steps but evidently you're too stupid to understand."

>>10451629
Yes, it’s still 80%. Maybe it wasn’t a taxi or the taxi was from another city, but the probability doesn’t change.

>>10460504
>0 blue taxis
>80% sure it was blue anyways
how stoned are you?
dumbest post itt

>>10460517
Go on man we can already tell you're too stupid to do this kind of probability, don't go showing people you can't even read either.

>>10460517
>it’s inconceivable that someone painted a taxi blue

>>10460536
>painted a taxi blue
>0 blue taxis
did i fucking stutter?

>>10460534
>i have no argument

>>10460548
"I tried to lead you to this with baby steps but evidently you're too stupid to understand."

>>10460545
>initial assumptions can’t be incorrect

>>10460553
Impressive, did you quote that from your PhD?

>>10460570
>being this mad

>>10460574
>i have no argument

>>10460580
>being THIS mad

>>10460605
>>10460580

>>10460614
>>10460605

>>10451629
Probably of being correct is still 80%, they just happened to fall in the 20% who were incorrect this time.

>>10460655
mark, someone separate this idiot from his money
He'd probably agree to play roulette without a ball, losing every bet

>>10460661
He's pointing out that even if 100% of cars are blue it's not impossible to be mistaken an swear you see a green or even red taxi 20% of the time

>>10460771
>not even wrong

>>10460795
>not even 23 chromosome pairs
Nigger people already brought up Bigfoot in this thread, Bigfoot and the loch Ness monster don't exist but the number of people who report seeing them isn't zero. The number of correct reports doesn't need to be related to the number of taxis even if 100% of taxis are one color.

Are you ESL or something? Really trying hard to figure out why you're this dense.

>>10461040
Fancy a game of roulette?

12 percent

>>10461040
>0 blue taxis
>"even so, some blue reporting is correct" hurr durr
topkek

>>10450038
You have to consider the probability that it was blue and they reported blue as well as the probability that it was green and they reported blue.

The former is obviously 80%, since they are correct 80% of the time. The latter is 100-80% = 20%. Thus we have 15×80% + 85×20% = 12 + 17% = 29%, as another anon has mentioned.

>>10462122
too bad the correct answer is 41.38%

>>10452339
>he said, with a spelling error
kek, erry time

>>10462122
>The former is obviously 80%
Incorrect, 80% is the chance that the witness will be correct given they've made such a statement. Since we know they've made such a statement, this is the chance that the taxi was blue.

>>10461821
If 0% of taxis are blue, the witness would still have to say green 80% of the time and blue 20% of the time to be consistent with the information given.

>>10462122
No. That is only if you're trying to calculate the average rate of blue taxi crime given a witness report. That's not what this situation is, you're being asked to consider the probability of exactly one such crime and told said probability is 80%.

>>10462756
I agree that the answer is 80% but your explanations and counterarguments make no sense. The average rate of blue taxi crime given a witness report is the same as the chance here. Just stop posting if you don't understand probability.

>>10449989
1/2 :^)

>>10449989
15%. What the other witnesses say is not relevant to this particular witness.

>>10462756
>information given
which wasn't "0% of taxis are blue"
duh

>>10462842
>other taxis in the city are not relevant to this particular taxi

>>10462792
>>10462792
Don't accuse others of not understanding probability when you can't see the difference between those two situations.

On the individual basis, which the OP is written for, we only take into account witness reliably so the probability is 80%.
If we considered the totality of a large number of taxi related crimes and assumed green and blue taxis are responsible for proportionate crime, then the frequency of actual blue taxi crime given it's reported as such is ~41% as the schizoposter above worked out. This is because a relatively small number of correctly reported blue taxi crime gets polluted by a relatively large number of incorrectly reported green crime. But these are only a factor considering the aggregate and not whether the individual reports are correct.

>>10451629
The witness might not know that 100% of the taxis are green so he/she could still get it wrong.

>>10462983
>On the individual basis, which the OP is written for, we only take into account witness reliably so the probability is 80%.
Witness reliability is based on general research of such situations, so you're not making any sense.

>If we considered the totality of a large number of taxi related crimes and assumed green and blue taxis are responsible for proportionate crime, then the frequency of actual blue taxi crime given it's reported as such is ~41% as the schizoposter above worked out.
No it's 80%. The 80% frequency is literally saying that out of all cases where a blue taxi is reported as being involved in a crime, 80% will actually involve a blue taxi. The frequency of blue and green taxis, their frequencies of being involved in a crime, and their frequencies of being reported are all subsumed by this statistic.

>>10462983
41% is an incorrect calculation, it has no meaning. It comes from the faulty interpretation that 80% is the chance of a taxi involved in a crime being reported as blue given it's blue (and the chance of being reported as green given it's green).
This is only equal to 80% when the probability of being reported as blue is equal to the probability of being blue. Since we have no way of knowing the former, we can't conclude this.

>>10463375
>>10463475
Individual case: Flip ONE weighted coin. You get the right call 80% of the time. You can do this coin flip as many times as you want and assess the out come as either right or wrong regardless of other factors to have a sample proportion that approaches the expectation of 80%. This is how you'd "research" this reliability rate.

Population case: A taxi involved crime occurs. IF you assume the rate of crime of the different taxi colors is proportionate to the number of blue vs green taxis, then first you flip a weighted coin to decide whether THIS crime was a blue or green taxi. The expectation is 15% blue, 85% green. Then, flip a different weighted coin to see if the report is accurate (80% expectation) or inaccurate (20% expectation). If you enumerate these contingencies, you will find the probability of the taxi being blue Given a witness statement of blue is ~41%. But, if you've read the thread, you'd already know I don't stand by this as a valid interpretation of the OP question as written.

>>10463522
Actually, I'd much rather say "you will find the frequency of the taxi..." than "probability" because the second approach is much more about describing a series of outcomes, where the first is the probability respecting exactly one outcome.

>>10463522
Your post is needlessly verbose and doesn't clarify anything. You have not shown me the distinction between the individual probability and the frequency among many events. They're the same thing.

The 41% number being faulty is solely due to the incorrect interpretation of which probability is 80%. It had nothing to do with this being an individual event vs. a group.

>>10463475
>equal to 80% when the probability of being reported as blue is equal to the probability of being blue
did it hurt when you pulled that bs out of your ass?

>>10463835
Clearer?

>>10463867
Wow you're dumb. This is literally the one thing you need to know to do conditional probability:

P(blue|reported blue) = P(blue) P(reported blue|blue) / P(reported blue)

Now please tell me under what circumstance P(blue|reported blue) = P(reported blue|blue) ? This might be a bit too complex for your skill level if you haven't passed the 5th grade yet.

>>10464023
How many times do I have to point out the same error you keep making? In order to multiply 1500 by 0.8 to get the number of blue taxis that are reported blue, 0.8 has to be the probability that a blue report will occur given the taxi is blue. But that's not what the question tells you. It tells you 0.8 is the opposite: the probability of a blue car given a blue report. So the only correct numbers there are the number of blue and green taxis.

>>10464133
>correct numbers
n=10000
1500.....1200.....300
8500.....1700.....6800
------------------------------
10000.....2900.....7100

fine, since you claim these are wrong
give the correct ones instead

please, no long lectures, just the numbers

>>10465472
Those numbers cannot be known from the information given. How do you not get this?

>>10465643
oh ok, so you claim it's a hoax, harassment, fake news

silly me
bye

>>10465667
No, it's just bad math.