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.)
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Question
For customers purchasing a refrigerator at a certain appliance store, let A be the
| 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.)
(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.)
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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