I have the following questionnaire:
Suppose the number of raisins in an English cake has a Poisson distribution with parameter 60. A player buys a cake, takes all the raisins one by one and divides the raisins between him and you as follows: after each raisin is extracted, he throws a balanced coin, giving you the raisin if it comes up heads, eating the raisin himself if it comes up tails. What is the distribution of the number of raisins you receive? The hope?
I can take the first distribution as Poisson and the second as Binomial. But how do I find the probability distribution when the distributions are not independent?