2.2.1 problem 33

(a)

$\frac{1}{2^{\left|C\right|}}$

(b)

${\left(\frac{1}{2}\right)}^{\left|A\right|}$

(c)

Let $p$ be a randomly selected person from $C$ sampled without replacement.

$P(p\in A\cup p\in B)=\frac{1}{2}+\frac{1}{2}-\frac{1}{4}=\frac{3}{4}$.

$P(A\cup B=C)={\left(P\right(p\in A\cup p\in B\left)\right)}^{\left|C\right|}={\left(\frac{3}{4}\right)}^{\left|C\right|}.$