A shopper is randomly selected from a market. Let A be the event the selected sh

Question

A shopper is randomly selected from a market. Let A be the event the selected shopper has a Visa credit card, and B be the event the shopper has a Mastercard credit card. Suppose P(A) = 0.5, P(B) = 0.45, and P(A B) = 0.8.

a. What is the probability that the shopper has neither type of card?

b. What is the probability that the shopper has both types of card?

c. What is the probability the individual has a Visa card but not a Mastercard? (Hint: You will use the answer from part b.)

d. Are the events of having a Visa card and a Mastercard mutually exclusive?

Explanation / Answer

a) P(Neither type of card) = 1 - P(A U B) = 1 - 0.8 = 0.2

b) P(Both type of cards) = P(A) + P(B) - P(A U B) = 0.5 + 0.45 - 0.8 = 0.15

c) P(Visa but not master card) = P(A) - P(Both type of cards) = 0.5 - 0.15 = 0.35

d) No, they aren't mutually exclusive because P(A and B) is not equal to 0.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.