Question

Consider randomly selecting a student at a large university, and let A be the event that...

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.

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