# Geometric distribution problem

danniim
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?

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!

danniim
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.

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.

danniim
Thanks! :)