Answer
a) {$C_{1}, C_{2}, C_{3}, C_{4}, C_{5}, C_{6}, C_{7}, C_{8}$}
b) $\frac{1}{4}$
c) $\frac{3}{4}$
Work Step by Step
Note that each outcome is equally likely and has a $\frac{1}{8}$ probability of occuring
a) Let $C_{n}$ denote cavity $n$.
$S =$ {$C_{1}, C_{2}, C_{3}, C_{4}, C_{5}, C_{6}, C_{7}, C_{8}$}
b) We are looking for $P(C_{1})+P(C_{2}) = \frac{1}{8} + \frac{1}{8} = \frac{2}{8} = \frac{1}{4}$
c) We are looking for $P(C_{3}\cup P(C_{4}') = 1 - P(C_{3}\cup P(C_{4}) = 1 - (\frac{1}{8} + \frac{1}{8}) = \frac{6}{8} = \frac{3}{4}$
