Chapter 5.3, Problem 2E

Let $X_1$ and $X_2$ be independent random variables with respective binomial distributions $b\left(3,\frac{1}{2}\right)$ and $b\left(5,\frac{1}{2}\right)$.

Determine

(a) $P\left(X_1=2,X_2=4\right)$.

(b) $P\left(X_1+X_2=7\right)$.