What is the Probability that Two Independent Coin Tossers Stop on the Same Toss?

[FaradayLaws]

Problem:
Suppose that the probability that a head appears when a coin is tossed is p and the probability that a tail occurs is q=1-p. Person A tosses the coin until the first head appears and stops. Person B does likewise. The results obtained by persons A and B are assumed to be independent. What is the probability that A and B stop on exactly the same number toss?

I am not quite sure how to solve this. I'm assuming that the tosses are distributed as a negative binomial and I'm lost as to how to put everything together.Please help !

Thanks!

 

[tiny-tim]

Hi FaradayLaws!

What is the probability that A and B stop on exactly the same number toss?

It's the sum from n = 1 to ∞ of the probability that A and B both stop on the nth toss.