Question

question
given ( p(a) = 0.3 ), ( p(b) = 0.57 ) and ( p(a \text{ and } b) = 0.251 ), find the value of ( p(b|a) ), rounding to the nearest thousandth, if necessary.
answer attempt 1 out of 2
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Explanation:

Step1: Recall Conditional Probability Formula

The formula for conditional probability is \( P(B|A) = \frac{P(A \cap B)}{P(A)} \).

Step2: Substitute Given Values

We know \( P(A \cap B) = 0.251 \) and \( P(A) = 0.3 \). Substitute these into the formula: \( P(B|A) = \frac{0.251}{0.3} \).

Step3: Perform the Division

Calculate \( \frac{0.251}{0.3} \approx 0.83666\ldots \).

Step4: Round to Nearest Thousandth

Rounding \( 0.83666\ldots \) to the nearest thousandth gives \( 0.837 \).

Answer:

\( 0.837 \)