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(B | A) = 0.81 P(C |An B') = 0.64 P(A) = 0.70 P(B | A) = 0.89 P(C |An B) = 0.76 P(C | A'n B) = 0.69 P(C | A'n B') = 0.31 (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. 10.7 C, 0.24 10.8 B', 0.11 e 10.6 A, 0.70 C, 0.36 0.6 0.3 A' C, 0.31 0.8 V 0.3 B', 0.19 0.6 (b) Compute P(A n Bn C). (Round your answer to four decimal places.) 0.47348 (c) Compute P(Bn C). (Round your answer to four decimal places.) 0.64115 (d) Compute P(C). (Round your answer to four decimal places.) (e) Compute P(A | B n 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(B | A) = 0.81 P(C |An B') = 0.64 P(A) = 0.70 P(B | A) = 0.89 P(C |An B) = 0.76 P(C | A'n B) = 0.69 P(C | A'n B') = 0.31 (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. 10.7 C, 0.24 10.8 B', 0.11 e 10.6 A, 0.70 C, 0.36 0.6 0.3 A' C, 0.31 0.8 V 0.3 B', 0.19 0.6 (b) Compute P(A n Bn C). (Round your answer to four decimal places.) 0.47348 (c) Compute P(Bn C). (Round your answer to four decimal places.) 0.64115 (d) Compute P(C). (Round your answer to four decimal places.) (e) Compute P(A | B n 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 First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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part 1, first problem. part 2, part d and e
![If P(B | A) > P(B), show that P(B' | A) < P(B'). [Hint: Add P(B' | A) to both sides of the given inequality and then use the fact that P(A | B) + P(A' | B) = 1.]
P(B | A) + P(B' | A) > P(B) + P(B' | A)
> P(B) + P(B' || A)
> P(B' | A)
V > P(B' | A)
P(B' | A) < P(B')
1 - P(B)
P(B')](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F781395ef-5933-4a4d-9640-3099b49e30d5%2Fa8bf763e-d654-4874-8c0c-85e089b7920b%2Fpz12b59_processed.png&w=3840&q=75)
Transcribed Image Text:If P(B | A) > P(B), show that P(B' | A) < P(B'). [Hint: Add P(B' | A) to both sides of the given inequality and then use the fact that P(A | B) + P(A' | B) = 1.]
P(B | A) + P(B' | A) > P(B) + P(B' | A)
> P(B) + P(B' || A)
> P(B' | A)
V > P(B' | A)
P(B' | A) < P(B')
1 - P(B)
P(B')
Transcribed Image Text: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(B | A') =
P(C | A n B') = 0.64
P(A) = 0.70
P(B | A) = 0.89
= 0.81
P(C | A n B) = 0.76
P(C | A'n B) = 0.69
P(C | A'n B') = 0.31
(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.
0.7
C', 0.24
B
0.8
в, 0.11
0.6
A, 0.70
C', 0.36
0.6
0.3
A'
с, 0.31
0.8
0.3
B', 0.19
0.6
(b) Compute P(A n B n C). (Round your answer to four decimal places.)
0.47348
(c) Compute P(B n C). (Round your answer to four decimal places.)
0.64115
(d) Compute P(C). (Round your answer to four decimal places.)
(e) Compute P(A | B n 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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