Stats question explanation

Let X1 and X2 be independent random variables with respective binomial distributions, b(3,1/2) and b(5,1/2).
Determine (a) P (X1 = 2, X2=4)
(b) P (X1 + X2 = 7)

I know the answers are a) 15/256 and b) 1/32 but can someone explain how this is done? I'm not understanding something

Spongebob Squarepants -

Since X1 and X2 are independent, simply multiply the probabilities:

P (X1 = 2, X2=4) = P(X1=2) x P(X2=4) = 15/256

(b) X1 + X2 is a Binomial with n = 3+5 = 8 and p = 1/2

P(X = 7) = 8C7 (1/2)^8 = 1/32

Hope that helped