Chapter 1.1, Problem 15E

Let $S=A_1\cup A_2\cup \mathrm{...}\cup A_m,$ where events $A_1,A_2,\mathrm{...},A_m$ are mutually exclusive and exhaustive.

(a) If $P\left(A_1\right)=P\left(A_2\right)=\mathrm{...}=P\left(A_m\right),$ show that $P\left(A_i\right)=\frac{1}{m},i=1,2,\mathrm{...},m$.

(b) If $A=A_1\cup A_2\cup \mathrm{...}\cup A_h,$ where $h<m$. and (a) holds, prove that $P\left(A\right)=\frac{h}{m}$.