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 had an icemaker, and C be the event that the customer purchased an extended warranty. Relevant probabilities are
P(A) = .75 P(B|A) = .9 P(B|Aʹ) = .8
P(C|A ⋂ B) = .8 P(C|A ⋂ Bʹ) = .6
P(C|Aʹ ⋂ B) = .7 P(C|Aʹ ⋂ Bʹ) = .3
a. Construct a tree diagram consisting of first-, second-, and third-generation branches, and place an event label and appropriate probability next to each branch.
b. Compute P(A ⋂ B ⋂ C).
c. Compute P(B ⋂ C).
d. Compute P(C).
e. Compute P(A|B ⋂ C), the probability of a U.S. purchase given that an icemaker and extended warranty are also purchased.