Events A₁ and A2 are mutually exclusive and form a complete partition of a sample space S with P (A₁) = 0.43. If E is an event in S with P (E | A₁) =0.17 and P(E|A₂) = 0.14, compute P(A₁ | E) =? (Hint: Because A₁ and A2 are mutually exclusive and form a complete partition of the sample space, P (A₂) = 1 − P (A₁) ). Note: If your final answer has up to four decimal places, please enter your full answer without rounding it. If your answer contains more than four decimal places, please round it to four decimal places before entering it in the box below.
Events A₁ and A2 are mutually exclusive and form a complete partition of a sample space S with P (A₁) = 0.43. If E is an event in S with P (E | A₁) =0.17 and P(E|A₂) = 0.14, compute P(A₁ | E) =? (Hint: Because A₁ and A2 are mutually exclusive and form a complete partition of the sample space, P (A₂) = 1 − P (A₁) ). Note: If your final answer has up to four decimal places, please enter your full answer without rounding it. If your answer contains more than four decimal places, please round it to four decimal places before entering it in the box below.
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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![Events \( A_1 \) and \( A_2 \) are mutually exclusive and form a complete partition of a sample space \( S \) with \( P(A_1) = 0.43 \). If \( E \) is an event in \( S \) with \( P(E \mid A_1) = 0.17 \) and \( P(E \mid A_2) = 0.14 \), compute \( P(A_1 \mid E) = ? \)
(Hint: Because \( A_1 \) and \( A_2 \) are mutually exclusive and form a complete partition of the sample space, \( P(A_2) = 1 - P(A_1) \)).
**Note:** If your final answer has up to four decimal places, please enter your full answer without rounding it. If your answer contains more than four decimal places, please round it to four decimal places before entering it in the box below.
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Transcribed Image Text:Events \( A_1 \) and \( A_2 \) are mutually exclusive and form a complete partition of a sample space \( S \) with \( P(A_1) = 0.43 \). If \( E \) is an event in \( S \) with \( P(E \mid A_1) = 0.17 \) and \( P(E \mid A_2) = 0.14 \), compute \( P(A_1 \mid E) = ? \)
(Hint: Because \( A_1 \) and \( A_2 \) are mutually exclusive and form a complete partition of the sample space, \( P(A_2) = 1 - P(A_1) \)).
**Note:** If your final answer has up to four decimal places, please enter your full answer without rounding it. If your answer contains more than four decimal places, please round it to four decimal places before entering it in the box below.
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