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According to​ Bayes' Theorem, the probability of event​ A, given that event B has​ occurred, is as follows.
Upper P left parenthesis Upper A vertical line Upper B right parenthesis equals StartFraction Upper P left parenthesis Upper A right parenthesis times Upper P left parenthesis Upper B vertical line Upper A right parenthesis Over Upper P left parenthesis Upper A right parenthesis times Upper P left parenthesis Upper B vertical line Upper A right parenthesis plus Upper P left parenthesis Upper A prime right parenthesis times Upper P left parenthesis Upper B vertical line Upper A prime right parenthesis EndFraction
Use​ Bayes' Theorem to find Upper P left parenthesis Upper A vertical line Upper B right parenthesis using the probabilities shown below.
Upper P left parenthesis Upper A right parenthesis equals one fourth
​, Upper P left parenthesis Upper A prime right parenthesis equals three fourths
​, Upper P left parenthesis Upper B vertical line Upper A right parenthesis equals one tenth
​, and Upper P left parenthesis Upper B vertical line Upper A prime right parenthesis equals one half

Respuesta :

Answer:

0.0625

Step-by-step explanation:

Data

  • P(A) = 1/4
  • P(A') = 3/4
  • P(B|A)= 1/10
  • P(B|A') = 1/2

The probability of event​ A, given that event B has​ occurred is computed with the following equation:

P(A|B) = [P(A)*P(B|A)]/[P(A)*P(B|A)+P(A')*P(B|A')]

Replacing with data:

P(A|B) = [1/4*1/10]/[1/4*1/10+3/4*1/2] = 0.0625

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