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 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 ??? ?). e. ?Compute P(A|B?C), the probability of a U.S. purchase given that an icemaker and extended warranty are also purchased.
Answer Step 1 of 5 a. Step 2 of 5 b. P(ABC)=0.75(0.9)(0.8)=0.54 Step 3 of 5 c. P(BC)= P(ABC)+ P(A’BC) =0.54+(0.25)(0.8)(0.7) =0.54+0.14=0.68