Question

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

31. Is possession of a Visa card independent of possession of a MasterCard? 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 it has a MasterCard?

		0.25
		0.12
		0.39
		0.48
		0.40

33.Is possession of an American Express card mutually exclusive of 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 different things

34.What is the probability of selecting a family that has either a 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 it has a Visa card?

		0.48
		0.12
		0.30
		0.20
		0.40

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

		0.25
		0.30
		0.55
		0.43
		0.12

Answer 1

Let M=master card ,V= visa card and A=American Express

P(M)=0.30 P(A)=0.20 and P(V)=0.25

P(M n A)=0.08 , P(M n V)=0.12 and P(A n V)=0.06

1. Is possession of a Visa card independent of possession of a MasterCard? Why or why not?

No since ,P(V|M)=P(V n M)/P(M) =0.12/0.30=0.40

but P(V)=0.25

Ans No, because P (V | M) ≠ P (V)

2. If a family has a Visa card, what is the probability that it has a MasterCard?

P(M|V)=P(M n V)/P(V)=0.12//0.25=0.48

Ans 0.48

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

No, because P (A ∩ V) ≠ .0000

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

P(V U A)=P(V)+P(A)-P(V n A)=0.25+0.20-0.06=0.39

Ans=0.39

5.If a family has a MasterCard, what is the probability that it has a Visa card

P(V|M)=P(V n M)/P(M)=0.12/0.30=0.4

Ans=0.4

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

P(V U M)=P(V)+P(M)-P(V n M)=0.25+0.30-0.12=0.43

Ans=0.43