Probability that a stone is cracked = 15/600; denote this event by .
Probability that a stone is discolored = 27/600; denote this event by .
Probability that a stone is neither cracked nor discolored = 562/600; in terms of and , this event is captured by .
a. We want to find . Use the known probability of its complement:
b. We want to find . By the inclusion-exclusion principle,
c. By the law of total probability,