Probability question - Binomial distribution

[thereddevils]

Homework Statement

A game is played by tossing two unbiased coins repeatedly until two heads are obtained in the same throw. The random variable X denotes the number of throws required. Find the expression for P(X=r).

Homework Equations

The Attempt at a Solution

It looks to be a binomial distribution but the number of trials could be infinity. I have no idea to class this into which distribution(so far i have learned binomial, poisson and normal).

The best i can get is

P(X=r)=nCr (1/4)^r (3/4)^(n-r)

 

[Office_Shredder]

What is n supposed to be?

The number if trials could be infinite, but the probability of that happening is zero. The setup is similar to if someone just flipped one coin until they got a heads; do you know how to solve that problem?

 

[thereddevils]

What is n supposed to be?

The number if trials could be infinite, but the probability of that happening is zero. The setup is similar to if someone just flipped one coin until they got a heads; do you know how to solve that problem?

It's an infinite geometric series probability(not sure what to call that).

1/2 + (1/2)^2 + (1/2)^3 + (1/2)^4 + ...

but now two coins are flipped together, i am not sure how to do that here.