Please show the step by step answer below for question 15,this is not assignment question.

ledies and nine dramas. Brian has seen five of the movies. If the first three movies he has seen are dramas, what is the probability that the last two are comedies? Assume that Brian chooses the shows at random and sees each movie at most once. 15. Conditional Probability Properties Let n be the sample space of an experiment, and let B be an event of S with P(B) > 0. Prove that (a) P(A| B) 2 0 for any event A C n; (b) P(Q B) = 1; (c) If Al, A2, . .. is a sequence of mutually exclusive events, then P ( UAilB ) = [P(AlB). i=1 i= 1 16. Defective and Nondefective Items If eight defective and 12 nondefective items are inspected one by one, at random and without replacement, what is the probability that (a) the first four items inspected are defective; (b) from the first three items at least two are defective