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?

 

[tiny-tim]

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.

 

[tiny-tim]

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 pq^n-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! :)