For customers purchasing a refrigerator at a certainappli
Chapter 2, Problem 63(choose chapter or problem)
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
\(\begin{array}{l} P(A)=.75 \quad P(B \mid A)=.9 \quad P\left(B \mid A^{\prime}\right)=.8\\ P(C \mid A \cap B)=.8 \quad P\left(C \mid A \cap B^{\prime}\right)=.6\\ P\left(C \mid A^{\prime} \cap B\right)=.7 \quad P\left(C \mid A^{\prime} \cap B^{\prime}\right)=.3 \end{array} \)
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 \(P(A \cap B \cap C)\).
c. Compute \(P(B \cap C)\).
d. Compute P(C).
e. Compute \(P(A|B \cap C)\), the probability of a U.S. purchase given that an icemaker and extended warranty are also purchased.
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