The prior probabilities for events A1 and Az are P(A1) = 0.40 and P(A2) = 0.60. It is also known that P(A,N A2) =0. Suppose P(B|A1)= 0.10 and P(B|A2) = 0.20. a. Are events A1 and A2 mutually exclusive? - Select your answer- Explain. (i) P(A1 N A2) = 0 (ii) P(A1) + P(A2) = 1 (iii) P(A2) * P (A2 | A1) (iv) P(A2) + P(A2 | A1) - Select your answer - b. Compute P(A n B) (to 2 decimals). Compute P(A2 n B) (to 2 decimals).

Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter11: Data Analysis And Probability
Section11.8: Probabilities Of Disjoint And Overlapping Events
Problem 2C
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The prior probabilities for events A, and Az are P(A1) = 0.40 and P(A2) = 0.60. It is also known that P(A, n A2)=0. Suppose P(B|A1) = 0.10 and P(B|A2) = 0.20.
a. Are events A1 and Ag mutually exclusive?
Select your answer-
Explain.
(i) P(A1 N A2) = 0
(ii) P(A1) + P(A2) = 1
(iii) P(A2) P (A2 | A1)
(iv) P(A2) = P(A2 | A1)
- Select your ans wer - ♥
b. Compute P(A1N B) (to 2 decimals).
Compute P(A2 nB) (to 2 decimals).
C. Compute P(B) (to 2 decimals).
Apply Bayes' theorem to compute P(A1 B) (to 4 decimals).
Also apply Bayes' theorem to compute P(A2|B) (to 4 decimals).
Transcribed Image Text:The prior probabilities for events A, and Az are P(A1) = 0.40 and P(A2) = 0.60. It is also known that P(A, n A2)=0. Suppose P(B|A1) = 0.10 and P(B|A2) = 0.20. a. Are events A1 and Ag mutually exclusive? Select your answer- Explain. (i) P(A1 N A2) = 0 (ii) P(A1) + P(A2) = 1 (iii) P(A2) P (A2 | A1) (iv) P(A2) = P(A2 | A1) - Select your ans wer - ♥ b. Compute P(A1N B) (to 2 decimals). Compute P(A2 nB) (to 2 decimals). C. Compute P(B) (to 2 decimals). Apply Bayes' theorem to compute P(A1 B) (to 4 decimals). Also apply Bayes' theorem to compute P(A2|B) (to 4 decimals).
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