An engineering consulting firm has two projects (which we will label as A and B) that it wants to work on in a forthcoming week, and because of limited resources it can work on only one project at a time. Project A will require more time than project B, and it is possible that neither project will be completed in a week. Let P(B|A) denote the probability that project B is completed within a week given that project A has been completed, and similarly define P(A|B). The head of the firm does not understand conditional probability and simply wants to know the chances of both projects being completed within the week.
(a) Can that be determined from what is given? Why or why not? Explain.
(b) Can this be determined if either P(A) or P(B) is known, without conditioning on the occurrence or nonoccurrence of the other event? Explain.