Question

question 7 - 1 point given that $p(b|a) = 0.88$ and $p(a) = 0.39$, what is $p(b \text{ and } a)$? round to three decimal places. provide your answer below:

Explanation:

Step1: Recall the formula for conditional probability

The formula for conditional probability is \( P(B|A) = \frac{P(B \text{ AND } A)}{P(A)} \), which can be rearranged to find \( P(B \text{ AND } A) \) as \( P(B \text{ AND } A) = P(B|A) \times P(A) \).

Step2: Substitute the given values

We are given \( P(B|A) = 0.88 \) and \( P(A) = 0.39 \). Substituting these values into the formula, we get \( P(B \text{ AND } A) = 0.88 \times 0.39 \).

Step3: Calculate the product

\( 0.88 \times 0.39 = 0.3432 \).

Step4: Round to three decimal places

Rounding \( 0.3432 \) to three decimal places gives \( 0.343 \).

Answer:

\( 0.343 \)