Have you worked out for this situation? If so is there a such that

?

Which is what would be required for to have a Geometric distribution.

Now the probability of a head on each toss is the same so has a geometric distribution. All you need do is calculate the probability of a head on a single toss.Suppose now that each time a coin is flipped, it is returned to the barrel and a coin is then selected at random from the three coins, what is the distribution of N?

CB