/sci/ - Science & Math

The coin is loaded.

ahahahahaAa!!

WHAT
THE
FUCK

INB4 http://en.wikipedia.org/wiki/Gambler%27s_fallacy

OP is correct, quiz answer is retarded.

The question is unclear. If they are talking about a fair coin, like they damn well should if they don't specifically say otherwise, your answer is correct. If they are talking about a coin that isn't necessarily fair, the .42 is correct-ish (though wrong in details).

>Based on these results

>>2620357
it's a retarded question which wants you not to assume a coins has equal chances for landing on either side

sorry

you are right

Suppose you toss a coin 2 times and get 2 heads and 0 tails. Based on these results, what is the probability that the next flip results in a tail?

but by chance a fair coin can come up 58 to 42.

its fairly likely.

like 90 to 10 would be very unlikely...
but with both so close to 50, i woudl presume the coin is fair, and not weighted.

>>2620391
0.0.0/0

I guess they're right, but that just means that the question is retarded.

Every flip is independent, and thus you are correct with your answer. Whoever administered that needs to read up on the gambler's fallacy.

>>2620391
by retard-quiz'z logic, 0%

>>2620391
lol. the question really should have been more clear.

those programs usually have a thing where you can contact the people who make the questions and report any broken, confusing, or wrong questions. look for it and report it

It didn't say fair coin. In all questions that ask you about coin tosses, it will specify if it's a fair coin.

That's my two cents...

You have to use Bayes theorem.

It might be that you typed it in wrong.

Damn online math courses :\

>>2620415
i think its logical to presume a coin is fair unless stated that it is unfair.

not the other way around.

There's no law of nature saying that a coin has exactly 50% chance of landing on either side. If you test out a specific coin and you get different results, those results are more valid than the assumption that there's a 50% chance either way.

>>2620421
*if you test out the coin an infinite number of times, then it is more valid

>FTFY

Well, I think the main part of the question is "based on these results." It's unclear, in any case, but I think that's where they got their answer.

>>2620425
>doesn't know shit about probability

Not surprising, since you study a soft science.

>>2620421
Every assignment I have ever had in my many years of schooling that dealt with a coin toss assumed the coin to be fair. Every assignment ever.

Based on the results, it's still 0.5. Fucking nigger quiz detected.

If you were actually testing the coin, you would define a confidence interval beforehand. The null hypothesis would probably be that the coin is fair, you can't claim that the coin is loaded based purely on the number of heads and tails.

Coin may be weighted
No mention of a fair coin
Based on results

sorry, OP, it's a retarded question but the way it's worded means that you are wrong in this case.

There is insufficient information to answer this question.

Each coin throw is independent of the previous one.
Without knowing if the coin is fair or not, you cannot determine any probabilities.

The answer 0.42 is not a probability, it's a statistical analysis.

>>2620384
This is all you need to know. You base the probability on the results, nothing else. You saw 42/100 flips give you a tails, so the probability is .42.

>>2620430
fuck you, i do know actually.
a coin isnt perfectly flat, so the air acting on it as it spins will be different on each side, which can very slightly alter the probability of which side it lands on.
and over an infinite number of times, this will not be exactly 50/50
(just very close)

also, i have read up on this just now, and apparently whichever face is face up on your thumb, is more likely to be face up after the flip as well, by slightly more than 50%, ergo, if you flip, and someone else calls it, increase the odds in your favour by placing the opposite of what they called face up vefore the flip.

and fuck you! insulting my intelligence...fucking faggot.

>>2620471
>whichever face is face up on your thumb, is more likely to be face up after the flip as well, by slightly more than 50%
I discovered that and promptly abused the shit out of it like 10 years ago when I played the Pokemon card game.

>>2620476
lol, nice!
:D

http://www.physorg.com/news175267656.html

" But first, here's what the researchers concluded: Using a high-speed camera that photographed people flipping coins, the three researchers determined that a coin is more likely to land facing the same side on which it started. If tails is facing up when the coin is perched on your thumb, it is more likely to land tails up.

How much more likely? At least 51 percent of the time, the researchers claim, and possibly as much as 55 percent to 60 percent -- depending on the flipping motion of the individual."

>>2620473
But that's wrong. 42/100 flips being tails doesn't make the probability 0.42; at best, it makes .42 the best *estimate* for the probability. You cannot deduce the probability of the coin from any number of results, only increasingly reliable estimates.

<div class="math">P(A|B) = \frac{P(B|A)P(A)}{P(B)}</div>

let A: getting 43 tails out of 101 tosses and B: getting 42 tails out of 100 tosses.

<div class="math">P(A) = \binom{101}{43} \frac{1}{2^{101}}</div>
<div class="math">P(B) = \binom{100}{43} \frac{1}{2^{100}}</div>

<span class="math">P(B|A) = 0.5[/spoiler], because if you have 42 tails out of 100 tosses, the next toss could be either tails (hence 43 tails out of 101 tosses, which is what you want) or heads (hence 42 tails out of 100 tosses, which you don't want).

Result <span class="math">P(B|A) \approx 0.59[/spoiler]. So, according to Mr. Bayes, you are both wrong.

Such a dumb question. If they wanted to test your knowledge on experimental probability, they should've just used pulling black and white marbles out of a box or something. If their goal was to fuck with you with "HAHA gotcha we never said it was a fair coin," they shouldn't be teaching stats at all.

>>2620489
All you could do is "estimate" the probability based on the data, like the problem asks. Pretty sure the point of the problem is demonstrate the value of doing a shitload of repetitions on these things to get an accurate probability.

>>2620491
what the fuck am I reading.eps

>>2620491
Fucking jsMath not supporting shit.

<div class="math">P(A) = \frac{101}{43} \frac{1}{2^{101}}</div>
<div class="math">P(B) = \frac{100}{43} \frac{1}{2^{100}}</div>

where the fraction is actually supposed to be the binomial coefficient, but jsMath doesn't like \binom, so...

>>2620491
Fucking jsMath not supporting shit.

<div class="math">P(A) = \frac{101}{43} \frac{1}{2^{101}}</div>
<div class="math">P(B) = \frac{100}{42} \frac{1}{2^{100}}</div>

where the fraction is actually supposed to be the binomial coefficient, but jsMath doesn't like \binom, so...

EDIT: because I suck at copypasta

>>2620486
Only 51-60%? For me it was closer to 90%. I guess having Lugia on one side of the coin and the logo on the other really screwed with the probabilities.

HEY FAGGOTS,

Read the pic.

>>2620517
>implying you aren't contributing to the problem by posting that picture

>>2620500
Although I admit I missed the "approximately" in the question, the question never mentions an estimate, and that doesn't follow from "approximately". After all, an estimate may be completely wrong (i.e. not even "approximately" correct) -- in particular, the results given do not imply that the the probability is approximately 0.42; it could we 0.8 for all we know with sufficiently good (or bad) luck.

If the coin was fair then the standard deviation for a 100 flip sample would be 2.5%. 42% is 3.2 standard deviations away from 50%. I'd say that's pretty good evidence the coin is not fair.

The standard deviation for 100 trials is 10. So chances are, with a fair coin, that there will be either 10 more or 10 less tails than 50. Considering that there were 42, I would say that the results were fairer than expected.

>>2620512
Dude you're seriously overthinking it. Assuming that they wanted to trick you by using an unfair coin without telling you the theoretical probability, the only probability that you can use is the experimental probability you have in front of you. No conditional probability or Bayes' theorem. P = .42

"BASED ON THESE RESULTS" MEANS STATISTICAL PROBABILITY.

THE DESIRED EVENT HAPPENED 42 TIMES IN 100 REPETITIONS. HENCE <span class="math">\displaystyle P(Tails)=\frac{42}{100} = 0.42[/spoiler]

IT'S NOT ROCKET SCIENCE

I HAVE SPOKEN. I ALSO MAD

>>2620540
>>2620545
Hivemind...but not...

Isn't it just the root of the number of the number of trials? Or am I retarded?

>>2620551
>I ALSO MAD
Not to mention wrong.

>>2620551
haha i was dumbfounded when reading all this shit about conditional probability... i couldn't have said that better myself

>>2620565
>conditional probability: right way to deal with something you don't know is fair or not
>this crap: wrong way

But apparently, they want the wrong way.

>>2620566

Yeah? Show me how I'm wrong. Bear in mind that the question was based solely on the data given, which is a 58:42 ratio in the coin tosses.

>>2620491
>>2620512
Why is <div class="math">P(B|A) = 0.5</div>? I'm pretty sure that <div class="math">P(A|B) = 0.5</div>, that's just the definition of a fair coin. Then it's

<span class="math">P(B|A) = \frac{P(A|B)P(B)}{P(A)}[/spoiler]

Come one OP. Even if the question is wrong you know what they were baiting for. It's better to be wrong and right than right and wrong.

>>2620573

Conditional probability is like the name suggest, conditional. Meaning the probability of some event A, given the occurrence of some other event B.

In a coin toss, one toss is not dependent of the other. Same goes with a die. You can make use of cond. prob. in a deck of cards for example, the odds of drawing an ace after 3 cards are already drawn is different from drawing an ace from an untouched deck. In other words, A given the occurrence of B versus A alone.

I hope you've understood

doesn't say a fair coin, and seems to infer the coin is not fair, and that the conclusion of an unfair coin can be substantiated by only 100 tosses

rubbish

>>2620573
They all have to whip our their e-dicks and prove how much more they know about statistics than anyone else here. Ignoring the fact that this is a retardedly easy question, of course.

Why is there a huge lack of lack of books on popular-chemistry? I don't believe I've ever seen one :(.

>>2620585
See >>2620489.

>>2620357

You don't need math people. You need English people.


>Based on these results
>Based on these results
>Based on these results
>Based on these results
>Based on these results
>Based on these results
>Based on these results
>Based on these results
>Based on these results
>Based on these results

>>2620611

I realize this, but again, the question specifically states "based on these results".

You don't just assume a fair coin in mathematics.

see >>2620500

>>2620573

All you need for this problem are these 2 posts.
>>2620551
>>2620546

The question is asking about your knowledge of experimental probability. If you don't know the real probability of getting heads or tails, the only way to approximate the next flip is by using your data. If you have 42 tails out of 100, it's correct to assume that your next flip has a approximately a 42% chance of being tails. The more times you flip the coin, the closer you will get to the actual probability, which is the law of large numbers.

>>2620357
The computer is right.
Stop being a dumbass!

>>2620635
I never said anything about fairness of coins. It's just that based on these results you cannot deduce ANYTHING about the probability of the coin with certainty. See >>2620531.

>>2620357
ITT OP bitches cause he sucks at math

>>2620639
>If you have 42 tails out of 100, it's correct to assume that your next flip has a approximately a 42% chance of being tails.
No, it is not. It is correct to estimate this number with high reliability, but incorrect to assume it is near 42%. After all, it might just be 80% with sufficiently bad luck. Unlikely, sure, but not impossible.

>>2620639

>>2620556
I think I got it wrong. It's 5% not 2.5%. My stats book the standard deviation of a sampling distribution of a sample proportion is the square root of (p(1-p)/n) where p is the proportion and n is the number of samples. That makes it 1.6 standard deviations. So this test would show results this far away from 50% 11% of the time. The evidence isn't as good as I thought.

>>2620650
>what dumb people actually believe

What class is this?

>>2620650

Okay, you have made it evident that you don't understand the concept of probability. Just stop.

>>2620639 is still correct, and you are wrong.
The beauty of mathematics is that it's not an opinion poll. You're wrong.

>>2620663
So which part of it do you challenge? Surely, you don't doubt that it COULD be the case that this particular coin has a 80% chance of getting tails? And based on that, I cannot escape the verdict that blindly assuming that 42% must be approximately correct must be wrong.

>>2620650
Based on the data, the data is not inaccurate. Based on the data, the chance is 42%. Trying to incorporate other shit is fucking stupid. You might as well say "well HURR da coin is a 50% chance" rather than your stupid statistical analysis (lol) bullshit. Based on the data means don't take anything but the data into account.

>>2620683
Again, which part do you think is wrong?

>>2620650
No fucking shit. Never once did I say the probability is .42. I said it's CORRECT to ASSUME based on your data. That little "sorry, that's not correct" message agrees with me. Coincidence?

Are you just trolling now?

>>2620687
>Based on the data, the data is not inaccurate.
The data is not inaccurate, but it certainly may be not representative.
>Based on the data, the chance is 42%.
No, based on the data, only the best ESTIMATE of the chance is 42%. There is a difference between the chance itself and our knowledge of the chance.
>Trying to incorporate other shit is fucking stupid. Based on the data means don't take anything but the data into account.
What, like probability theory?

>>2620696
In mathematics, it is never correct to assume something that may be wrong.
>That little "sorry, that's not correct" message agrees with me. Coincidence?
No -- it probably also doesn't have a proper mathematical background.

>>2620690

The part where you ignore "If you don't know the real probability of getting heads or tails, the only way to approximate the next flip is by using your data. If you have 42 tails out of 100, it's correct to assume that your next flip has a approximately a 42% chance of being tails. The more times you flip the coin, the closer you will get to the actual probability, which is the law of large numbers."

I don't know how to rephrase it more simply, so I'll just use his version.

In mathematics, you don't just assume a fair coin. With a 42% probability, yes, either heads or tails can happen. You could even flip tails 20 times in a row. But with a 42%prob. as the repetitions approach infinity/a number sufficiently large, the ratio of heads/tails also approaches 42/100.

Yes, we know that *really* the ratio would approach 1/2, but this is statistical/experimental probability, and based on the given data, 42% is correct.

>>2620711

>>2620720
>If you don't know the real probability of getting heads or tails, the only way to approximate the next flip is by using your data.
Correct so far.
>If you have 42 tails out of 100, it's correct to assume that your next flip has a approximately a 42% chance of being tails.
No. If you replace "assume" by "estimate", your claim becomes valid, but it its current form it's just plain wrong.

>Yes, we know that *really* the ratio would approach 1/2, but this is statistical/experimental probability, and based on the given data, 42% is correct.
A correct estimate, yes. Not the correct chance.

>>2620711
If you're the OP, or someone else in a basic stat course, I feel bad for you at this point. You will certainly fail if this is a concept that you need to keep arguing about.

But then again, maybe I'm gullible as shit. And if that's the case, I'll console myself by knowing that I have a BA in statistics.

>>2620742
>Assumes reality has to model math, instead of math modeling reality

You should teach a course in trollin!

OP, you are right. What the fuck is this shit? Whoever is teaching this needs to be lynched.

>>2620742
Ok. Point taken. Replace assume with estimate.

>>2620742

You're slipping into semantics with the assume/estimate thingy you've got going on there.

Assuming an approximate result in mathematics, is basically estimating.

>>2620776

OP is not right. You need to be lynched.

Read the fucking thread.

>>2620794
>You're slipping into semantics with the assume/estimate thingy you've got going on there.
True, but semantics are important - particularly in probability theory and statistics, where it's very common to derive a correct result but interpret it in a completely wrong way.
>Assuming an approximate result in mathematics, is basically estimating.
Except that "estimating" leaves room for gross error (you're conscious of the fact that you may be completely wrong), whereas "assuming an approximate" does not (you're only conscious of small errors there, not gross ones -- the possibility that the coin might just actually have a 80% chance is accounted for in the "estimate", but not in the "approximate assumption").

Jesus christ, people: This is a question about EMPIRICAL PROBABILITY.

Educate yourselves:
http://regentsprep.org/Regents/math/ALGEBRA/APR5/theoProp.htm

tl;dr: Yes the theoretical probability is 50/50, but the empirical probability must be calculated based on actual observed occurrences.

>>2620858
We're no longer talking about the very-simple answer to the question. Sorry if you're mad about it.

>>2620858
LOL, I didn't even read your whole post when I posted the last message. Way to yell at people and be wrong at the same.

It should also be pointed out that the estimate of the probability is not unique. For example, 43/102 is also a valid estimate of the probability (this is the Bayesian expectation value with uniform prior).

>>2620672
OP here, class is basic University statistics, Math 1530.