Chapter 1.2, Problem 18E

For each positive integer n, let $P\left(\left\{n\right\}\right)={\left(\frac{1}{2}\right)}^n$.

Consider the events $A=\left\{n:1\le n\le k\right\},B=\left\{n:1\le n\le 10\right\},$ and $C=\left\{n:6\le n\le 10\right\}$.

Find (a) $P\left(A\right)$, (b) $P\left(B\right)$.

(c) $P\left(A\cup B\right)$ (d) $P\left(A\cap B\right)$, (e) $P\left(C\right)$, and (I) $P\left(B’\right)$.