The prior probabilities for events A1 and A2 are P(A1) = .45 and P(A2) = .55. It is alsoknown that P(A1 ∩ A2) = 0. Suppose P(B ∣ A1) = .05 and P(B ∣ A2) = .20.a. Are A1 and A2 mutually exclusive? Explain.b. Compute P(A1 ∩ B) and P(A2 ∩ B).c. Compute P(B).d. Apply Bayes’ theorem to compute P(A1 ∣ B) and P(A2 ∣ B). 1. The prior probabilities for events A1 and A2 are P(A1) = .45 and P(A2) = .55. It is alsoknown that P(A1 N A2) = 0. Suppose P(B |A1) = .05 and P(B | A2) = .20.a. Are A1 and A2 mutually exclusive? Explain.b. Compute P(A1 N B) and P(A2 n B).c. Compute P(B).d. Apply Bayes' theorem to compute P(A1 | B) and P(A2 | B).

Given that P(A1) = 0.45, P(A2) = 0.55 P(B|A1) = 0.05, P(B|A2) = 0.20 Note : According to our…

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Áre A1 and A2 mutually exclusive? Explain. Compute P(A1 N B) and P(A2 n B). Compute P(B).

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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Question

The prior probabilities for events A1 and A2 are P(A1) = .45 and P(A2) = .55. It is also
known that P(A1 ∩ A2) = 0. Suppose P(B ∣ A1) = .05 and P(B ∣ A2) = .20.
a. Are A1 and A2 mutually exclusive? Explain.
b. Compute P(A1 ∩ B) and P(A2 ∩ B).
c. Compute P(B).
d. Apply Bayes’ theorem to compute P(A1 ∣ B) and P(A2 ∣ B).

1. The prior probabilities for events A1 and A2 are P(A1) = .45 and P(A2) = .55. It is also
known that P(A1 N A2) = 0. Suppose P(B |A1) = .05 and P(B | A2) = .20.
a. Are A1 and A2 mutually exclusive? Explain.
b. Compute P(A1 N B) and P(A2 n B).
c. Compute P(B).
d. Apply Bayes' theorem to compute P(A1 | B) and P(A2 | B).

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