According to Bayes' Theorem, the probability of event A, given that event B has occurred, is as follows. P(A) P(B| A) P(A) • P(B| A) + P (A') •P(B| A') P(A| B) = Use Bayes' Theorem to find P(A| B) using the probabilities shown below. 1 P(A) =. P(A') = P(B| A) = , and P(B| A') = - 10 The probability of event A, given that event B has occurred, is P(A| B) =| %3D
According to Bayes' Theorem, the probability of event A, given that event B has occurred, is as follows. P(A) P(B| A) P(A) • P(B| A) + P (A') •P(B| A') P(A| B) = Use Bayes' Theorem to find P(A| B) using the probabilities shown below. 1 P(A) =. P(A') = P(B| A) = , and P(B| A') = - 10 The probability of event A, given that event B has occurred, is P(A| B) =| %3D
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![According to Bayes' Theorem, the probability of event A, given that event B has occurred, is as follows.
\[
P(A | B) = \frac{P(B | A) \cdot P(A)}{P(A) \cdot P(B | A) + P(A') \cdot P(B | A')}
\]
Use Bayes' Theorem to find \( P(A | B) \) using the probabilities shown below.
\[
P(A) = \frac{2}{3}, \quad P(A') = \frac{1}{3}, \quad P(B | A) = \frac{1}{7}, \quad \text{and} \quad P(B | A') = \frac{7}{10}
\]
The probability of event A, given that event B has occurred, is \( P(A | B) = \boxed{\phantom{number}} \).
(Round to the nearest thousandth as needed.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2da5533f-8665-454a-8786-e097ba2bf066%2F89a9b61e-7645-4f9b-9ea7-654efcb9941a%2Fozwd62l_processed.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.
\[
P(A | B) = \frac{P(B | A) \cdot P(A)}{P(A) \cdot P(B | A) + P(A') \cdot P(B | A')}
\]
Use Bayes' Theorem to find \( P(A | B) \) using the probabilities shown below.
\[
P(A) = \frac{2}{3}, \quad P(A') = \frac{1}{3}, \quad P(B | A) = \frac{1}{7}, \quad \text{and} \quad P(B | A') = \frac{7}{10}
\]
The probability of event A, given that event B has occurred, is \( P(A | B) = \boxed{\phantom{number}} \).
(Round to the nearest thousandth as needed.)
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