Hi,
There are three people, A, B ,C, tossing a coin. The first one to get heads wins, they toss in succession in the order ABC, show the probability of A winning is 4/7.
I thought that the probability of A winning would be the sum from n=1 to inf. of (1/2)^4n.. as each time 3 tails have to be thrown and then either another tail or head.

Is this correct? If so, how can I get a value of 4/7?
Thanks

A tosses on 1st, 4th, 7th, ... etc round. So A wins if and only if the first head appears on 1st, or 4th, or 7th, or ... etc round.

Assuming the coin is fair and each toss is independent.

Currently your series is the probability of first head appears on 4th, 8th, 12th, ... etc round; so it is not the solution of the problem. Try to correct it; and the remaining part will just be a simple infinite geometric series.