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...

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.