The number of flowers N appearing on an apple tree, is a random variable with distribution

for some . Each flower turns into a fruit with probability independently of other flowers on the tree. Given that there are apples on the tree what is the probability that there were flowers originally on the tree?

Here's my solution (I am not sure, so please correct me if I'm wrong):

Bayes' theorem says:

In this example A is the event: 'originally there were flowers on the tree'. B is the event: 'there are apples on the tree.

So in the numerator of the Bayes' formula we get:

and for the denominator we get:

since there are r choose n ways in total and each has probability . Is this correct? Please reply.....