Assume P(A) = 0.3, P(B|A) = 0.75, P(B|A') = 0.20, P(C\AnB) = 0.20, P(C|A'nB) = 0.15, P(C|AnB') = 0.80, and P(C|A' ÓB') = 0.90. (a) Find P(An BnC). (b) Find P(B' nC). (c) Find P(C).
Assume P(A) = 0.3, P(B|A) = 0.75, P(B|A') = 0.20, P(C\AnB) = 0.20, P(C|A'nB) = 0.15, P(C|AnB') = 0.80, and P(C|A' ÓB') = 0.90. (a) Find P(An BnC). (b) Find P(B' nC). (c) Find P(C).
A First Course in Probability (10th Edition)
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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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Transcribed Image Text:2.90 Pollution of the rivers in the United States has
been a problem for many years. Consider the following
events:
A: the river is polluted,
B: a sample of water tested detects pollution,
C: fishing is permitted.
0.7
B
0.95
0.9
A
D
0.8
Figure 2.10: Diagram for Exercise 2.92.
Transcribed Image Text:Assume P(A) = 0.3, P(B|A) = 0.75, P(B|A') = 0.20,
P(C\ANB) = 0.20, P(C\A'nB) = 0.15, P(C|ANB') =
0.80, and P(C|A' ń B') = 0.90.
( a) Find P(Αn Β n C).
(b) Find P(B' nC).
(c) Find P(C).
(d) Find the probability that the river is polluted, given
that fishing is permitted and the sample tested did
not detect pollution.
%3D
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