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

distribution P[N = n]=p^n . Assume that a

flower turns into a fruit with probability Alpha (binomial distribution)

Given that there is a number r of apples on the tree, what is the probability that originally there were n flowers on it?

my thinking

Conditional P[r apples / n flowers]=binomial distribution = P (r apples Joint n flowers)/P(n flowers)

here I can get P (r apples Joint n flowers) in terms of the other two known expressions

Conditional P [n flower / r apples] = P (r apples Joint n flowers)/P(r flowers)

is there a way of calculating p (r flowers)? I cannot draw out the diff between venn diagrams of p (r flowers) and P[r apples / n flowers]