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) = 0.74 P(B | A) = 0.85 P(B | A') = 0.82 P(C | A ∩ B) = 0.76 P(C | A ∩ B') = 0.55 P(C | A' ∩ B) = 0.75 P(C | A' ∩ B') = 0.25 (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) = 0.74 P(B | A) = 0.85 P(B | A') = 0.82 P(C | A ∩ B) = 0.76 P(C | A ∩ B') = 0.55 P(C | A' ∩ B) = 0.75 P(C | A' ∩ B') = 0.25 (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.)
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter11: Data Analysis And Probability
Section11.8: Probabilities Of Disjoint And Overlapping Events
Problem 2C
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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) = 0.74 | P(B | A) = 0.85 | P(B | A') = 0.82 |
P(C | A ∩ B) = 0.76 | P(C | A ∩ B') = 0.55 | |
P(C | A' ∩ B) = 0.75 | P(C | A' ∩ B') = 0.25 |
(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.)
(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.)
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