Coin flipping

gegrad · June 5th, 2008, 5:05 pm

A jar has one 2-headed coin (both sides Head) and 9 fair coins.You pick a coin at random and flip it 10 times, and get all heads.What is the probability that you flipped the 2-headed coin ?Am I doing it right ?where

(10H|BC) = 1P(BC) = 1/10P(10H|fair) = (.5)^10P(fair) = 9/10

quantyst · June 6th, 2008, 7:50 am

Hi gegrad,You are on target! Just fine!I saw a problem very similar to this one elsewhere on Wilmott. Go to: http://www.wilmott.com/messageview.cfm? ... adid=61626

quantyst · June 6th, 2008, 8:01 am

To elaborate...There are two different random variables or processes involved, one is the selection of the coin, the second the tossing of that coin. So, if we let c denote the random coin selection, and T(c,i) denote the i-th tossing of the coin c, then the question can be stated as follows:P{c=BC | T(c,i)=H for i=1, 2, ..., 10} = ? The rest would be the same as yours, while using this new notation. A conscious and explicit specification of all relevant random variables goes a long way in solving the problem.

Curves · November 13th, 2008, 10:03 am

in my opinion the probability that you picked the 2 headed coin is 1/10. reason: the observation HHH..H only means that you cannot eliminate the possibility that you picked the biased coin. HH...H can occur with the unbiased coin as well.if the question had been that, given x% confidence what is the probability that you picked the biased coin then you can do a ztest i suppose?

quantyst · November 13th, 2008, 10:11 am

QuoteOriginally posted by: Curvesin my opinion the probability that you picked the 2 headed coin is 1/10. reason: the observation HHH..H only means that you cannot eliminate the possibility that you picked the biased coin. HH...H can occur with the unbiased coin as well.if the question had been that, given x% confidence what is the probability that you picked the biased coin then you can do a ztest i suppose?Boy, boy!I'd love to make wagers with you. Where do you exist?

Curves · November 13th, 2008, 3:55 pm

accept i was wrong, thank you for pointing out.if it is a wager then it is possible that i might just be lucky, very very lucky!

quantyst · November 13th, 2008, 5:31 pm

QuoteOriginally posted by: Curvesaccept i was wrong, thank you for pointing out.if it is a wager then it is possible that i might just be lucky, very very lucky!Allow me to increase your luck!We'll make it 5 to 1. Every time a head comes up I win $1, you lose $1, and every time a tail comes up I lose $5, and you win $5. Do you feel lucky now?