[Guest]

your friend has a challenge for you. he sets up a game. one coin is double heads, the other is standard head tails. you are blind folded. he flips the heads tails con and places the two coins in a random order. you pick left or right. the blind fold is then removed. if the coin you picked currently shows tails, the game starts over. if the coin you pick shows heads, the coin is turned over. if tails on the other side, you win, if heads, you lose.

what would be the probability of winning?

I'll give my two answers Sunday at around noon.

[Guest]

Probability of winning a single game = probability of picking the heads on the std coin = 1/2 * 1/2 = 1/4

Probability of game being repeated = probability of picking tails = 1/4

Probability of winning 2nd game = 1/4*1/4

Probability of game being repeated again = 1/4*1/4

Probability of winning 3rd game = 1/4*1/4*1/4

overall probability = sum of all above = 1/4 + (1/4)² + (1/4)³ + ....... + (1/4)ⁿ, where n is infinity and (1/4)^infinity = 0

I am poor at Maths, so I will stop here. But, I believe the result will be approx ~ 32%

Edited July 10, 2010 by HB921

[Guest]

Probability of winning a single game = probability of picking the heads on the std coin = 1/2 * 1/2 = 1/4

Probability of game being repeated = probability of picking tails = 1/4

Probability of winning 2nd game = 1/4*1/4

Probability of game being repeated again = 1/4*1/4

Probability of winning 3rd game = 1/4*1/4*1/4

overall probability = sum of all above = 1/4 + (1/4)² + (1/4)³ + ....... + (1/4)ⁿ, where n is infinity and (1/4)^infinity = 0

I am poor at Maths, so I will stop here. But, I believe the result will be approx ~ 32%

the infinite sum of (1/a)^n = 1/(a-1), where n starts at 1. so the exact answer is 1/3

Edited July 10, 2010 by klose

[Guest]

While blind folded, you have no reason to pick left over right or vice versa, so you have 50% chance of getting double sided coin or 50% chance of getting head-tails. Picking the heads-tails you have 50% chance of getting tails which means from the start of the game there is a 25% chance of restarting. What of the other 75%? Well 2/3's of this corresponds to you picking the double-sided coin and losing, which corresponds to 50% from the start of the game. The remaining 1/3 of the 75% corresponds to you picking the heads-tails coin when it is heads and winning.

So from the beginning, we have

50% chance to lose

25% chance to win

25% chance to try again

The probability of winning is

probability of winning on first try

+ prob of getting try again and winning on second try

+ prob of getting try again twice and winning on third try

+ ...

= 0.25 + 0.25*0.25 + 0.25*0.25+0.25 + ...

= 0.25(1 + 0.25 + 0.25^2 + ...)

= 0.25 * 1/(1-0.25) = 0.25/0.75 = 1/3

Edit: Cool, I guess everyone agrees with me, or vice versa.

Edited July 10, 2010 by mmiguel1

[Guest]

You cannot win if the HT coin comes up tails in a particular round. The only way to win is if both coins come up heads, and you pick the correct one. In any given round, you have a 1/4 chance of getting 2 heads, and a 1/2 chance of guessing the correct coin, so you have a 1/8 chance of winning in any particular round. The probability of losing in any particular round is simply the probability that you pick the HH coin, or 1/2. Thus, as it is the only other possibility, we have a 3/8 chance of starting over after a particular round. Thus, your probability of winning = P(round 1 win) + P(round 2 win) + P(round 3 win) + ... = 1/8 + 3/8*1/8 + 3/8*3/8*1/8 + ..., which is a geometric series with sum 1/8*(1/(1-3/8)) = 1/8 * 8/5 = 1/5.

[Guest]

Chuck:

"My solution...don't think anyone's gotten it yet...']You cannot win if the HT coin comes up tails in a particular round. The only way to win is if both coins come up heads, and you pick the correct one. In any given round, you have a 1/4 chance of getting 2 heads, and a 1/2 chance of guessing the correct coin, so you have a 1/8 chance of winning in any particular round. The probability of losing in any particular round is simply the probability that you pick the HH coin, or 1/2. Thus, as it is the only other possibility, we have a 3/8 chance of starting over after a particular round. Thus, your probability of winning = P(round 1 win) + P(round 2 win) + P(round 3 win) + ... = 1/8 + 3/8*1/8 + 3/8*3/8*1/8 + ..., which is a geometric series with sum 1/8*(1/(1-3/8)) = 1/8 * 8/5 = 1/5."

----------------------

I will follow the same steps you took:

Yes, you cannot win that particular round if a tails comes up, but you can win if you pick the tails and win in a following round.

You do not have a 1/4 chance of getting 2 heads in a round because

one of the coins is double sided and will always be heads.

You actually have a 1/2 chance of getting 2 heads in a round.

You have 1/2 of a chance of guessing the HT coin and 1/4 chance winning in a round. You have a 1/4 chance of starting over in a round. Geometric series gives 1/3.

Edited July 10, 2010 by mmiguel1

[Guest]

i honestly don't know if anyone is on the right track with their answers. geometric serieces is probably right but it would have to be an alternating geometric series. if all esle fails you could do the ratio test to see if it is a series but i am way too drunk right now to do this so drunk infact that someone is typing this for me.

honestly right now i just want to dance. are you still typin gthis you should probably stop. oh i love this track, you really can't blame the jackson five for what happened to michael

i felt everyone should see this guys logic/mindset before taking his advice into consideration

[Guest]

i honestly don't know if anyone is on the right track with their answers. geometric serieces is probably right but it would have to be an alternating geometric series. if all esle fails you could do the ratio test to see if it is a series but i am way too drunk right now to do this so drunk infact that someone is typing this for me.

honestly right now i just want to dance. are you still typin gthis you should probably stop. oh i love this track, you really can't blame the jackson five for what happened to michael

i felt everyone should see this guys logic/mindset before taking his advice into consideration

you have opened my eyes

[Guest]

Could you not exclude picking the one showing tails, as it would start over the game?

[Guest]

Could you not exclude picking the one showing tails, as it would start over the game?

I think phillip meant that it starts over a round of the game, not the game itself, but maybe you are right. I don't think it will change the outcome though.

Probability of winning, given no restarts = 0.25/(0.25 + 0.5) = 1/3

[Guest]

I agree with the posted answers, and just wanted to add that this reminds me a lot of Genetics (the whole Aa,AA stuff)

[Guest]

answer has to be 1/3 i thinks very correct...

[Guest]

If you measure the probability before the blindfold was removed then you have 25% win, 50% lose, 25% play again.

If you measure the probablity after blindfold was removed and you saw heads, then you have 33.333...% chance to win.

I agree with most answers

Does BD have some sort of private time zone I'm not aware of? If a member whose country isn't specified says s/he'll post an answer at noon, when does s/he plan to post it? I'd guess "American" time, but the US is so big it has a few time zones...

Edited July 11, 2010 by Arbelle