Question

For customers purchasing a refrigerator at a certain appliance store, let A be the event that the refrigerator was manufactured in the U.S., B be the event that the refrigerator has an icebreaker, and C the event that the customer purchased an extended warranty.

Relevant probabilities are:

P(A) = 0.75

P(B|A) = 0.9

P(B|A′) = 0.8

P(C|A ∩ B) = 0.8.

P(C|A ∩ B′) = 0.6

P(C|A′ ∩ B) = 0.7

P(C|A′ ∩ B′) = 0.3

a. What is the probability that the refrigerator was manufactured in the US, with an icebreaker, and the customer purchased an extended warranty?

b. What is the probability that the refrigerator does not have an icebreaker or the customer did not purchase an extended warranty?

c. What is the probability that the customer purchased an extended warranty?

d. What is the probability that the refrigerator does not have an icebreaker given that it was not manufactured in the US?

Answer 1

Ans:

a. What is the probability that the refrigerator was manufactured in the US, with an icebreaker, and the customer purchased an extended warranty?

P(A n B n C)=P(C|A n B)*P(A n B)

=0.75*0.9*0.8

=0.54

b. What is the probability that the refrigerator does not have an icebreaker or the customer did not purchase an extended warranty?

P(B n C)=P(A n B n C) +P(A' n B n C)

=0.54+(0.25*0.8*0.7)

=0.68

c. What is the probability that the customer purchased an extended warranty?

P(C)=P(A n B n C) +P(A' n B n C)+P(A n B' n C) +P(A' n B' n C)

=0.54+0.045+0.14+0.015

=0.74

d. What is the probability that the refrigerator does not have an icebreaker given that it was not manufactured in the US?

P(A|B n C)=P(A n B n C)/P(B n C)

=0.54/0.68

  =0.7941