Consider randomly selecting a student at a large university, and let A be the event that the selected student has a Visa card and B be the analogous event for MasterCard. Suppose that P(A) = .6 and P(B) = .4.
a. Could it be the case that P(A ∩ B) = .5? Why or why not?
b. From now on, suppose that P(A ∩ B) = .3. What is the probability that the selected student has at least one of these two types of cards?
c. What is the probability that the selected student has neither type of card?
d. Describe, in terms of A and B, the event that the selected student has a Visa card but not a MasterCard, and then calculate the probability of this event.
e. Calculate the probability that the selected student has exactly one of the two types of cards.