Answer:
We have that
.
So

However, b is a probability, which means that it cannot be negative. So no, P(A ∩ B) cannot be 0.5. It can, at most, be 0.3.
Step-by-step explanation:
Event A:
Probability that a student has a Visa card.
Event B:
Probability that the student has a MasterCard.
We have that:

In which a is the probability that a student has a Visa card but not a MasterCard and
is the probability that a student has both these cards.
By the same logic, we have that:

In this problem, we have that:

(a) Could it be the case that P(A ∩ B) = 0.5?
We have that
.
So

However, b is a probability, which means that it cannot be negative. So no, P(A ∩ B) cannot be 0.5. It can, at most, be 0.3.