Chapter 2: Problem 47 (page 82) 47. Return to the credit card scenario of Exerci

Question

Chapter 2: Problem 47 (page 82) 47. Return to the credit card scenario of Exercise 12 (Sec tion 2.2), and let C be the event that the selected student has an American Express card. In addition to P(A) ,6, P(B) = .4, and P(A n B) .3, suppose that P(C) = .2, a. What is the probability that the selected student has at least one of the three types of cards? b. What is the probability that the selected student has both a Visa card and a MasterCard but not an American Express card? c. Calculate and interpret P(B A) and also PA B) d. If we learn that the selected student has an American Express card, what is the probability that she or he also has both a Visa card and a MasterCard? Given that the selected student has an American Express card, what is the probability that she or he has at least one of the other two types of cards? e.

Explanation / Answer

as P(A U B) =P(A)+P(B)-P(A n B)

a)

b) probability =P(AnB) -P(AnBnC) = 0.3-0.08 =0.22

c) P(B|A) =P(A nB) /P(A) =0.3/0.6 =0.5 =probability of having master card given has Visa,

P(A|B) =P(A n B)/P(B) =0.3/0.4 =0.75 =probability of having Visa card given has master card

d)

probability= P(AnBnC)/P(C) =0.08/0.2 =0.4

e)probability =(P(AnC)+P(BnC)-P(AnBnC))/P(C) =(0.15+0.1-0.08)/0.2=0.85

P(A)= 0.6 P(B)= 0.4 P(C)= 0.2 P(AnB)= 0.3 P(BnC)= 0.1 P(AnC)= 0.15 P(AUB)= 0.7 P(BUC)= 0.5 P(AUC)= 0.65 P(AnBnC) = 0.08

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

---

---

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