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
4 years, 1 month 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?

- 4 years, 1 month ago

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

- 4 years, 1 month ago

Cheers!From where did you get this question?

- 4 years, 1 month ago

Actually the question struck to my mind when my sir was teaching us conditional probability.its a generalized version I managed to frame. :P

- 4 years, 1 month ago

OHk!

- 4 years, 1 month ago