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) = 0.6 and P(B) = 0.3. (a) Could it be the case that P(A ∩ B) = 0.5? Why or why not? [Hint: For any two sets A and B if A is a subset of B then P(A) ≤ P(B).]

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.

a line is an defined derm because it

a)contains an infinite number of points b) can be used to create other geometric shapes c)describes something that does not have width or depth d) is a term that does not have a formal definition. a line is an undefined term because it: contains an infinite number of points.

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step-by-step explanation: vsfdvsfvd