According to Bayes' Theorem, the probability of event A, given that event B has occurred, is as follows: \[ P(A|B) = \frac{P(A) \cdot P(B|A)}{P(A) \cdot P(B|A) + P(A^{'}) \cdot P(B|A^{'})} \] Use Bayes' Theorem to find \( P(A|B) \) using the probabilities shown below. \[ P(A) = \frac{5}{6}, \quad P(A^{'}) = \frac{1}{6}, \quad P(B|A) = \frac{1}{10}, \quad \text{and} \quad P(B|A^{'}) = \frac{7}{10} \] --- The probability of event A, given that event B has occurred, is \( P(A|B) = \square \). (Round to the nearest thousandth as needed.)
According to Bayes' Theorem, the probability of event A, given that event B has occurred, is as follows: \[ P(A|B) = \frac{P(A) \cdot P(B|A)}{P(A) \cdot P(B|A) + P(A^{'}) \cdot P(B|A^{'})} \] Use Bayes' Theorem to find \( P(A|B) \) using the probabilities shown below. \[ P(A) = \frac{5}{6}, \quad P(A^{'}) = \frac{1}{6}, \quad P(B|A) = \frac{1}{10}, \quad \text{and} \quad P(B|A^{'}) = \frac{7}{10} \] --- The probability of event A, given that event B has occurred, is \( P(A|B) = \square \). (Round to the nearest thousandth as needed.)
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![According to Bayes' Theorem, the probability of event A, given that event B has occurred, is as follows:
\[ P(A|B) = \frac{P(A) \cdot P(B|A)}{P(A) \cdot P(B|A) + P(A^{'}) \cdot P(B|A^{'})} \]
Use Bayes' Theorem to find \( P(A|B) \) using the probabilities shown below.
\[ P(A) = \frac{5}{6}, \quad P(A^{'}) = \frac{1}{6}, \quad P(B|A) = \frac{1}{10}, \quad \text{and} \quad P(B|A^{'}) = \frac{7}{10} \]
---
The probability of event A, given that event B has occurred, is \( P(A|B) = \square \).
(Round to the nearest thousandth as needed.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F508ee786-e013-45c0-a264-dadcc72c168c%2F3b710739-9f5c-4051-bc37-bcc30ecb9171%2Fbb5g78h.jpeg&w=3840&q=75)
Transcribed Image Text:According to Bayes' Theorem, the probability of event A, given that event B has occurred, is as follows:
\[ P(A|B) = \frac{P(A) \cdot P(B|A)}{P(A) \cdot P(B|A) + P(A^{'}) \cdot P(B|A^{'})} \]
Use Bayes' Theorem to find \( P(A|B) \) using the probabilities shown below.
\[ P(A) = \frac{5}{6}, \quad P(A^{'}) = \frac{1}{6}, \quad P(B|A) = \frac{1}{10}, \quad \text{and} \quad P(B|A^{'}) = \frac{7}{10} \]
---
The probability of event A, given that event B has occurred, is \( P(A|B) = \square \).
(Round to the nearest thousandth as needed.)
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