# 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
2 years, 9 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?

- 2 years, 9 months ago

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

- 2 years, 9 months ago

Cheers!From where did you get this question?

- 2 years, 9 months 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

- 2 years, 9 months ago

OHk!

- 2 years, 9 months ago

Comment deleted Oct 08, 2015

I am not aware of the answer. Could you please post you work?

- 2 years, 9 months ago

Comment deleted Oct 08, 2015

Oh the problem is not supposed to be like that..wait let me specify it.sorry for it.

- 2 years, 9 months ago

No problemo!

- 2 years, 9 months ago