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A sample is selected from one of two populations, S₁ and S₂, with P(S₁) = 0.8 and P(S₂) = 0.2. The probabilities that an event A occurs, given that event S₁ or S₂ has occurred are P(A|S₁) = 0.2 and P(A|S₂) = 0.1. Use the Law of Total Probability to find P(A).

A sample is selected from one of two populations, S₁ and S₂, with P(S₁) = 0.8 and P(S₂) = 0.2. The probabilities that an event A occurs, given that event S₁ or S₂ has occurred are P(A|S₁) = 0.2 and P(A|S₂) = 0.1. Use the Law of Total Probability to find P(A).

College Algebra
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter9: Counting And Probability
Section9.4: Expected Value
Problem 1E: If a game gives payoffs of $10 and $100 with probabilities 0.9 and 0.1, respectively, then the...
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A sample is selected from one of two populations, 
S1 and S2,
 with 
P(S1) = 0.8
 and 
P(S2) = 0.2.
 The probabilities that an event A occurs, given that event 
S1
 or 
S2
 has occurred are
P(A|S1) = 0.2
 and 
P(A|S2) = 0.1.
Use the Law of Total Probability to find 
P(A)
 
A sample is selected from one of two populations, s, and S,, with P(S,) = 0.8 and P(S,) = 0.2. The probabilities that an event A occurs, given that event s, or s, has occurred are P(A|S,) = 0.2 and P(A|S2) = 0.1. Use the Law of Total Probability to find P(A).
Transcribed Image Text:A sample is selected from one of two populations, s, and S,, with P(S,) = 0.8 and P(S,) = 0.2. The probabilities that an event A occurs, given that event s, or s, has occurred are P(A|S,) = 0.2 and P(A|S2) = 0.1. Use the Law of Total Probability to find P(A).
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