Probability Challenge!

Ai;i=1,2,3..nA_{i};i=1,2,3..n are nn persons which play a game of tossing a coin. The game starts when A1A_{1} tosses the coin. If he gets a tail, the next person i.e. A2A_{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 rth{r}^{th} person i.e. ArA_{r} wins the game.

Note by Rohit Ner
4 years ago

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The probability that the game is played again is 12n\dfrac{1}{2^{n}}.The probability that the r th person wins in the x th round of the game is 12xn+r\dfrac{1}{2^{xn+r}}.Hence the answer,according to me should be,x=112xn+r\sum_{x=1}^{\infty}\dfrac{1}{2^{xn+r}}. This is a simple G.P. What do you think?

Adarsh Kumar - 4 years ago

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oh yeah! i too got the same answer! cheers!

Rohit Ner - 4 years ago

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Cheers!From where did you get this question?

Adarsh Kumar - 4 years 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 - 4 years ago

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@Rohit Ner OHk!

Adarsh Kumar - 4 years ago

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