Answer to Question #43478 in Statistics and Probability for Casey Marshall

Question

I have a biased coin that lands heads with probability p and start with an empty urn. I flip the coin n times. Each time the coin lands heads, I add a blue ball to the urn. Each time the coin lands tails, I add a green ball to the urn. After I finish flipping the coin and without knowing the composition of the urn, you draw k balls from the urn one at a time, replacing each ball you draw before drawing another one. If all k of the balls that you draw are blue, what is the probability that all n balls in the urn are blue?