a. Compute the probability that the selected individual has at least one of the

Question

a. Compute the probability that the selected individual has at least one of the two types of cards (i.e., the probability of the event ).

b. What is the probability that the selected individual has neither type of card?

c. Describe, in terms of A and B, the event that the selected student has a Visa card but not a MasterCard, and then calculate the probability of this event.

12. Consider randomly selecting a student at a certain univer- sity, and let A denote the event that the selected individual has a Visa credit card and B be the analogous event for a MasterCard. Suppose that PA) .5, PCB 4, and P(An B 25

Explanation / Answer

a) P(At least one card)

= P(A or B)

= P(A) + P(B) - P(A B)

= 0.5 + 0.4 - 0.25

= 0.65

b) P(Neither type of card)

= 1 - P(At least one card)

= 1 - 0.65

= 0.35

c) P(Visa card but not a MaterCard)

= P(A Bc)

= P(A) - P(A B)

= 0.5 - 0.25

= 0.25

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