Question

symbolic probability rules
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question
given ( p(a) = 0.52 ), ( p(b) = 0.75 ) and ( p(a \text{ and } b) = 0.46 ), find the value of ( p(a|b) ), 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 \( P(A|B) = \frac{P(A \cap B)}{P(B)} \), where \( P(A \cap B) \) is the probability of both \( A \) and \( B \) occurring, and \( P(B) \) is the probability of \( B \) occurring.

Step2: Substitute Given Values

We are given \( P(A \cap B) = 0.46 \) and \( P(B) = 0.75 \). Substitute these values into the formula: \( P(A|B) = \frac{0.46}{0.75} \).

Step3: Calculate the Result

Perform the division: \( \frac{0.46}{0.75} \approx 0.613333\ldots \)

Step4: Round to Nearest Thousandth

Rounding \( 0.613333\ldots \) to the nearest thousandth gives \( 0.613 \).

Answer:

\( 0.613 \)