joint probability question

Hi!Can someone please help me with these 2 questions?

Thanks in advance!

1) The number of people entering the drugstore in a given hour is a Poisson random variable with parameter 10. Compute the conditional probability that at most 3 men entered the drugstore, given that 10 women entered in that hour. What assumptions have you made?

2) Let

f(x,y) = 24xy 0 ≤ x ≤ 1, 0 ≤ y ≤ 1, 0 ≤ x+y ≤ 1

0 otherwise

Show that f(x,y) is a joint probability density function and find E(X).