For any two events A and B, if P(A|B) = 0.6 and P(B|A) = 0.4, then what is the value of P(A)/P(B) ?
1.5
We are given \(P(A\mid B) = 0.6\) and \(P(B\mid A) = 0.4\), and we need to find \(\dfrac{P(A)}{P(B)}\).
By the definition of conditional probability:
\(P(A\mid B) = \dfrac{P(A\cap B)}{P(B)}\) and \(P(B\mid A) = \dfrac{P(A\cap B)}{P(A)}\).
Dividing the first by the second, the common factor \(P(A\cap B)\) cancels:
\(\dfrac{P(A\mid B)}{P(B\mid A)} = \dfrac{P(A\cap B)/P(B)}{P(A\cap B)/P(A)} = \dfrac{P(A)}{P(B)}\).
Therefore \(\dfrac{P(A)}{P(B)} = \dfrac{0.6}{0.4} = 1.5\).
Hence, the correct answer is 1.5.
Important Questions from Conditional Probability
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