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Probability Challenge!

\(A_{i};i=1,2,3..n\) are \(n\) persons which play a game of tossing a coin. The game starts when \(A_{1}\) tosses the coin. If he gets a tail, the next person i.e. \(A_{2}\) gets a chance to toss the coin and so on. Whosoever gets a head first wins the game. If no one wins, the game is played again. Find the probability of event in which the \({r}^{th}\) person i.e. \(A_{r}\) wins the game.

Note by Rohit Ner
1 year, 3 months ago

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The probability that the game is played again is \(\dfrac{1}{2^{n}}\).The probability that the r th person wins in the x th round of the game is \(\dfrac{1}{2^{xn+r}}\).Hence the answer,according to me should be,\(\sum_{x=1}^{\infty}\dfrac{1}{2^{xn+r}}\). This is a simple G.P. What do you think? Adarsh Kumar · 1 year, 3 months ago

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@Adarsh Kumar oh yeah! i too got the same answer! cheers! Rohit Ner · 1 year, 3 months ago

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@Rohit Ner Cheers!From where did you get this question? Adarsh Kumar · 1 year, 3 months ago

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@Adarsh Kumar Actually the question struck to my mind when my sir was teaching us conditional probability.its a generalized version I managed to frame. :P Rohit Ner · 1 year, 3 months ago

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@Rohit Ner OHk! Adarsh Kumar · 1 year, 3 months ago

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Comment deleted Oct 08, 2015

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@Adarsh Kumar I am not aware of the answer. Could you please post you work? Rohit Ner · 1 year, 3 months ago

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Comment deleted Oct 08, 2015

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@Adarsh Kumar Oh the problem is not supposed to be like that..wait let me specify it.sorry for it. Rohit Ner · 1 year, 3 months ago

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@Rohit Ner No problemo! Adarsh Kumar · 1 year, 3 months ago

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