Given P, left parenthesis, A, right parenthesis, equals, 0, point, 5P(A)=0.5, P, left parenthesis, B, right parenthesis, equals, 0, point, 3, 3P(B)=0.33 and P, left parenthesis, A, and , B, right parenthesis, equals, 0, point, 2, 4, 5P(A and B)=0.245, find the value of P, left parenthesis, B, vertical bar, A, right parenthesisP(B∣A), rounding to the nearest thousandth, if necessary.
Question
Given P, left parenthesis, A, right parenthesis, equals, 0, point, 5P(A)=0.5, P, left parenthesis, B, right parenthesis, equals, 0, point, 3, 3P(B)=0.33 and P, left parenthesis, A, and , B, right parenthesis, equals, 0, point, 2, 4, 5P(A and B)=0.245, find the value of P, left parenthesis, B, vertical bar, A, right parenthesisP(B∣A), rounding to the nearest thousandth, if necessary.
Solution
To find the value of P(B|A), we use the formula for conditional probability, which is P(B|A) = P(A and B) / P(A).
Given in the problem, we have:
P(A) = 0.5 P(B) = 0.33 P(A and B) = 0.245
Substituting these values into the formula, we get:
P(B|A) = 0.245 / 0.5 = 0.49
So, P(B|A) = 0.49, rounded to the nearest thousandth.
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