Chapter 1.4, Problem 3E

Let A and B be independent events with $P\left(A\right)=\frac{1}{4}$ and $P\left(B\right)=\frac{2}{3}$.

Compute (a) $P\left(A\cap B\right)$, (b) $P\left(A\cap B\text{'}\right)$, (c) $P\left(A\text{'}\cap B\text{'}\right)$, (d) $P\left[\left(A\cap B\right)\text{'}\right]$, and (e) $P\left(A\text{'}\cap B\right)$.