In a certain city, 30% of the families have a MasterCard, 20%have an American Express card, and 25% have a Visa card. Eightpercent of the families have both a MasterCard and an AmericanExpress card. Twelve percent have both a Visa card and aMasterCard. Six percent have both an American Express card and aVisa card.

31. Is possession of a Visa card independent of possession of aMasterCard? Why or why not?

		No, because P (M | V) ? P (V)
		No, because P (V | M) ? P (V)
		Yes, because P (M) = P(V)
		Yes, because P (V ? M) ? 0
		No, because Visa and MasterCard are different things

32. If a family has a Visa card, what is the probability that ithas a MasterCard?

		0.25
		0.12
		0.39
		0.48
		0.40

33.Is possession of an American Express card mutually exclusiveof possession of a Visa card? Why or why not?

		No, because P (A ? V) ? P (V)
		Yes, because P (A ? V) = .0000
		No, because P (A ? V) ? .0000
		Yes, because P (V ? A) ? P (A)
		No, because American Express and Visa card are differentthings

34.What is the probability of selecting a family that has eithera Visa card or an American Express card?

		0.25
		0.20
		0.37
		0.33
		0.39

35.If a family has a MasterCard, what is the probability that ithas a Visa card?

		0.48
		0.12
		0.30
		0.20
		0.40

36.What is the probability of selecting a family that has eithera Visa card or a MasterCard?

		0.25
		0.30
		0.55
		0.43
		0.12