It is known that bowl A₁ contains three red and seven blue chips and bowl A₂ contains eight red and two blue chips. All chips are identical in size and shape. A die is cast and bowl A₁ is selected if five or six spots show on the side that is up; otherwise, bowl A2 is selected. The selected bowl is handed to another person and one chip is taken at random. Suppose that this chip is red, an event which we denote by B. Find the probability of A₁ being selected and the probability of A2 being selected given that the chip is red (P(A₁ |B), P(A₂|B))

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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It is known that bowl A₁ contains three red and seven blue chips and bowl A₂ contains eight red and two blue chips. All
chips are identical in size and shape. A die is cast and bowl A₁ is selected if five or six spots show on the side that is up;
otherwise, bowl A2 is selected. The selected bowl is handed to another person and one chip is taken at random. Suppose
that this chip is red, an event which we denote by B. Find the probability of A₁ being selected and the probability of A₂
being selected given that the chip is red (P(A₁ |B), P(A₂|B))
Transcribed Image Text:It is known that bowl A₁ contains three red and seven blue chips and bowl A₂ contains eight red and two blue chips. All chips are identical in size and shape. A die is cast and bowl A₁ is selected if five or six spots show on the side that is up; otherwise, bowl A2 is selected. The selected bowl is handed to another person and one chip is taken at random. Suppose that this chip is red, an event which we denote by B. Find the probability of A₁ being selected and the probability of A₂ being selected given that the chip is red (P(A₁ |B), P(A₂|B))
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It is required to find the probability of bowl A1 being selected given that the chip is red, P(A1|B), and the probability of bowl A2 being selected given that the chip is red, P(A2|B).

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