Question

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) = 0.7 and P(B) = 0.4.(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).]

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.

the answer is A ∩ B'

Calculate the probability of this event.

E) Calculate the probability that the selected student has exactly one of the two types of cards.

Answer #1

**Answer:**

**a)**

**b)**

P(at least one) = P(A)+P(B) -P(A n B)

= 0.7+0.4-0.2

=0.9

**c)**

P(neither ) =1-0.9

=0.1

**d)**

P(A n B') =P(A)-P(A n B)

= 0.7-0.2

= 0.5

**e)**

P(exactly one) =P(A)+P(B) -2*P(A n B)

= 0.7+0.4-2*0.2

=0.7

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