Professor Smith gives his lectures in T - shirts of three colors: gray, red, and blue. For each lecture ( independently of others ) , he chooses gray with probability 0 . 5 , red with probability 0 . 3 , and blue with probability 0 . 2 . There are 9 lectures in April. ( a ) What is the probability that he wears T - shirts of each color three times in April? ( b ) What is the probability that he wears a gray T - shirt exactly 8 times in April