# Geometric distribution problem

Can anyone solve this for me? I think it is geometric distribution.

Tom, Dick and Harry play .the following game. They toss a fair coin in
turns. First Tom tosses, then Harry, then Dick, then Tom again and so on
until one of them gets a Head and so becomes the winner. What is the
probability that Tom wins?

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tiny-tim
Homework Helper
Welcome to PF!

Hi danniim! Welcome to PF! Show us what you've tried, and where you're stuck, and then we'll know how to help! Hi tiny-tim,

Okay well my main problem is that I don't know what formula to use.

I thought you would use p(q)^x-1 where p is the probability of success(0.5) and q is the probability of failing (0.5), x is supposed to be the number of trials ie the number of times the coin is tossed but this is not given. This leaves me with the following:

0.5(0.5)^x-1 = ?..... two unknowns.

So clearly I am not understanding something in the question.

tiny-tim
Homework Helper
I thought you would use p(q)^x-1 where p is the probability of success(0.5) and q is the probability of failing (0.5), x is supposed to be the number of trials ie the number of times the coin is tossed …
Hi danniim! (use n, not x, for numbers, and try using the X2 tag just above the Reply box )

Yes, you use pqn-1 for the probability of the game finishing on the nth toss.

Now add up for all the n's that make Tom the winner. Thanks! :)