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2 answers:
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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.