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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 below. P(A) = 0.76      P(B | A) = 0.85     P(B | A') = 0.75 P(C | A ∩ B) = 0.84 P(C | A ∩ B') = 0.61 P(C | A' ∩ B) = 0.69 P(C | A' ∩ B') = 0.32 (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). (Round your answer to four decimal places.) (c) Compute P(B ∩ C). (Round your answer to four decimal places.) (d) Compute P(C). (Round your answer to four decimal places.) (e) Compute P(A | B ∩ C), the probability of a U.S. purchase given that an icemaker and extended warranty are also purchased. (Round your answer to four decimal places.)

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 below. P(A) = 0.76      P(B | A) = 0.85     P(B | A') = 0.75 P(C | A ∩ B) = 0.84 P(C | A ∩ B') = 0.61 P(C | A' ∩ B) = 0.69 P(C | A' ∩ B') = 0.32 (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). (Round your answer to four decimal places.) (c) Compute P(B ∩ C). (Round your answer to four decimal places.) (d) Compute P(C). (Round your answer to four decimal places.) (e) Compute P(A | B ∩ C), the probability of a U.S. purchase given that an icemaker and extended warranty are also purchased. (Round your answer to four decimal places.)

College Algebra
College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
Publisher:Ron Larson
Chapter8: Sequences, Series,and Probability
Section8.7: Probability
Problem 5ECP: In Example 5, what is the probability that an institution selected at random is in the Pacific...
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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 below.

P(A) = 0.76      P(B | A) = 0.85     P(B | A') = 0.75
P(C | A ∩ B) = 0.84 P(C | A ∩ B') = 0.61
P(C | A' ∩ B) = 0.69 P(C | A' ∩ B') = 0.32
(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). (Round your answer to four decimal places.)


(c) Compute P(B ∩ C). (Round your answer to four decimal places.)


(d) Compute P(C). (Round your answer to four decimal places.)


(e) Compute P(A | B ∩ C), the probability of a U.S. purchase given that an icemaker and extended warranty are also purchased. (Round your answer to four decimal places.)
 
 
(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. A, 0.76 2 B B', 0.15 B', 0.25 C', 0.16 C', 0.39 C', 0.31
Transcribed Image Text:(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. A, 0.76 2 B B', 0.15 B', 0.25 C', 0.16 C', 0.39 C', 0.31
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