3.97 A company places a rush order for wire of two thicknesses.

Consignments of each thickness are to be sent immediately when they are available. Previous experience suggests that the probability is 0.8 that at least one of these consignments will arrive within a week. It is also estimated that, if the thinner wire arrives within a week, the probability is 0.4 that the thicker wire will also arrive within a week. Further, it is estimated that, if the thicker wire arrives within a week, the probability is 0.6 that the thinner wire will also arrive within a week.

a. What is the probability that the thicker wire will arrive within a week?

b. What is the probability that the thinner wire will arrive within a week?

c. What is the probability that both consignments will arrive within a week?