/sci/ - Science & Math

[Anonymous No.1819412]

Ok /sci/, I hate hw threads as much as you do but I have debated this problem with nearly every person in my college statistics class and we all keep coming up with different answers and I don't know where else to turn.

A Bag contains 3 coins, one of which has heads on BOTH sides. A coin is chosen randomly and tossed 3 times the outcomes are recorded then the coin is replaced in the bag WITHOUT KNOWING whether it was the two headed coin.

a) what is probability the number of heads exceeds tails?
b) probability exactly 3 heads?
c) probability at least 1 tails?

If someone can shed some light on this than I will either post all my coupons, post all my info pics, or dump porn (I'll link to /s/ here)

[Anonymous No.1819426]

bumping w/ thermite

[Anonymous No.1819436]

There are only 17 possible outcomes.

Just list 'em and count 'em up.

[Anonymous No.1819439]

>>1819436
Forget I said that. 24 outcomes.

[Anonymous No.1819446]

coin 1 hhh,hht,hth,htt,thh,tht,tth,ttt
coin 2 hhh,hht,hth,htt,thh,tht,tth,ttt
coin 3 hhh,hhh,hhh,hhh,hhh,hhh,hhh,hhh

[Anonymous No.1819449]

>>1819439
ok that sounds more like it. Im working on it but I have to come up with some kind of formula for it.

[Anon No.1819465]

a is harder...so i'll tackle b.
there are 8 combinations for 2 of the coins:
HHH
HTH
HHT
HTT
THH
THT
TTH
TTT
and 1 combination for the other:
HHH
=
the probability of getting 3 heads with a regular coin is 1/8. and the probability of getting 3 heads with the crazy coin is 1/1. so weight it out:
2*(1/3)*(1/8)+(1/3)*(1/1)= 41.66666%
===
same applies to c.
7 out of 8 for the reg coins, and 0 for crazy coin:
2*(1/3)*(7/8)+(1/3)*0=58.3333%


no?

[Anonymous No.1819475]

>A coin is chosen randomly and tossed 3 times the outcomes are recorded then the coin is replaced in the bag WITHOUT KNOWING whether it was the two headed coin.

from my understanding, does this mean to say "A coin is selected from the bag, flipped three times, and then removed from the bag. Then, a normal coin is put into the bag."

that's the only logical connection i can ascertain with this.

anyway, you want p(h > t).

you have a 1/3 chance of choosing each coin from the bag.

If the selected coin is the trick coin, then you have a 100% probability of getting h > t.

total prob so far: 1/3

Two coins have fair odds for both sides. Probability of getting h > t is p(h, h, t) + p(h, t, h) + p(t, h, h) + p(h, h, h). each of those is (1/2)*(1/2)*(1/2), so 1/8, * 4 for each of those = 1/2

that means all coins together probability is (1/3)*(1) + (1/3)*(1/2) + (1/3)*(1/2) -> 1/3 + 1/3 -> Therefore, P(h > t) is 2/3.

then for b, exactly 3 heads, well firstly 100% thus 1/3 for the trick coin. then, getting p(h,h,h) for the two good coins, (1/8) each. so p(h = 3) is (1/3)*(1) + (1/3)*(1/8) + (1/3)*(1/8) -> 8/24 + 1/24 + 1/24 -> 10/24 therefore the probability of 3 heads exactly is 5/12.

lastly, it's easier to solve c by taking the inverse situation. instead of at least 1 tails, we will calculate probability of no tails, and then subtract by 100% or 1.

we already know the probability of 0 tails, since that's also the probability of getting 3 heads.

therefore, c) = 1 - 5/12 = 7/12

i think that's it

[Anonymous No.1819482]

>>1819465
wait, for b, if you use the logic behind >>1819446 that does not make sense, wouldnt it be 3/24?

I got the same answer for c though

[Anonymous No.1819484]

>>1819465
yes that's right. refer to >>1819475 as your percents are the same as the rationals listed

[Anon No.1819488]

>>1819482
i did use the same logic. i gave it a *2 multiplier to signify the equality of the 2 regular coins out of the 3.

[Anonymous No.1819489]

>>1819475
sorry, i meant "subtract FROM 100% or 1", not by.

[Anonymous No.1819491]

>>1819475
>from my understanding, does this mean to say "A coin is selected from the bag, flipped three times, and then removed from the bag. Then, a normal coin is put into the bag."
>and then removed from the bag. Then, a normal coin is put into the bag

sorry no

pick a random coin, flip it 3 times, record data, replace in bag w/o knowing which coin it was

[Anonymous No.1819497]

>>1819491
yeah well, you obviously didn't really read it quite right because that's the same damn thing. it doesn't matter what's put back into the bag since you're not recording anything after that point are you? all that matters is that you take a coin out of a bag, one of them is a trick coin with only heads, and that you don't know which coin you took.

"sorry no"...

[Anonymous No.1819499]

ok since you guys are helping im gonna start posting some info

[Anon No.1819501]

>>1819475
but i think your a-part is right.
.33333 chance per coin to pick, 1/1 chance of satisfying (a) if crazy coin, .5 chance if reg coin.
so
2*(1/3)*.5+(1/3)*(1)=66.66666%
=
2/3, as suspected by intuition. congratulate your statistics class on being dumber than 4chan haha

[Anonymous No.1819505]

>>1819497
I suppose it doesnt matter now that I think about it
my apologies

[Anonymous No.1819508]

>>1819499
just telling you

i literally gave you the answer to the question here >>1819475

the answer is

a) 2/3 or 66.667%
b) 5/12 or 41.667%
c) 7/12 or 58.333%

you can take the answers or not using the proof i showed you, though i know it's correct since i've done questions like this hundreds of times before. it's your choice.

[sage No.1819521]

>>1819446

The answer is already right here. Just do the arithmetic.

[Anonymous No.1819530]

moar info

thx guys I got it
much appreciated

[Anonymous No.1819531]

>>1819501
>dumber than 4chan

to be honest, that's not that relevant. this is 12th grade of high school level probability (well only because they dont even touch probability past the flipping of a few coins and their outcomes in elementary school). most people could answer this question if they're in the right mindset. i'm a little surprised OP and his/her classmates couldn't figure it out since it's really quite simplistic, but at the same time i understand since it's rather esoteric if you don't think mathematically, which i suspect OP doesn't (business major? uh i dunno just guessing)

[Anonymous No.1819533]

[Anonymous No.1819540]

>>1819531
its easy to figure if you just write out all outcomes, that wasnt the problem. For the problem we have to answer it showing only formulas, which from writing out all outcomes it was much easier to figure out. I'm a sophomore in college...and yes I know this must be retard math for some of you

[Anonymous No.1819542]

not animooted

[Anonymous No.1819545]

>>1819540
Mammals are on the bottom.

[Anonymous No.1819548]

and btw not business major, biology major here, specifically botany

[Anonymous No.1819552]

>>1819545
no shit man its in ascending order by level of complexity

[Anonymous No.1819555]

last one

thx again

[Anonymous No.1819561]

>>1819555
WTF? 590 robberies using a syringe? That's just fucked up.

[Anonymous No.1819587]

>>1819555

So, my multi-tool will get me fined 8k then?