Question

question
given ( p(a) = 0.56 ), ( p(b) = 0.7 ) and ( p(a|b) = 0.64 ), find the value of ( p(a \text{ and } b) ), rounding to the nearest thousandth, if necessary.
answer attempt 1 out of 2
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Explanation:

Step1: Recall the formula for conditional probability

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. We can rearrange this formula to solve for \( P(A \cap B) \): \( P(A \cap B) = P(A|B) \times P(B) \).

Step2: Substitute the given values into the formula

We are given that \( P(A|B) = 0.64 \) and \( P(B) = 0.7 \). Substituting these values into the formula, we get:
\( P(A \cap B) = 0.64 \times 0.7 \)

Step3: Calculate the product

Calculating \( 0.64 \times 0.7 \), we have:
\( 0.64 \times 0.7 = 0.448 \)

Answer:

\( 0.448 \)