Question

question
given that ( p(a \text{ and } b) = 0.29 ) and ( p(a|b) = 0.67 ), what is ( p(b) )?
give your answer as a percent. round final answer to two decimal places.
provide your answer below:
□%

Explanation:

Step1: Recall the multiplication rule for conditional probability

The formula for conditional probability is \( P(A|B) = \frac{P(A \text{ AND } B)}{P(B)} \). We can rearrange this formula to solve for \( P(B) \).

Step2: Rearrange the formula to solve for \( P(B) \)

Starting with \( P(A|B) = \frac{P(A \text{ AND } B)}{P(B)} \), we can multiply both sides by \( P(B) \) to get \( P(A|B) \times P(B) = P(A \text{ AND } B) \). Then, divide both sides by \( P(A|B) \) to solve for \( P(B) \): \( P(B) = \frac{P(A \text{ AND } B)}{P(A|B)} \).

Step3: Substitute the given values into the formula

We know that \( P(A \text{ AND } B) = 0.29 \) and \( P(A|B) = 0.67 \). Substituting these values into the formula, we get \( P(B) = \frac{0.29}{0.67} \).

Step4: Calculate the value of \( P(B) \)

\( \frac{0.29}{0.67} \approx 0.4328 \). To convert this to a percentage, we multiply by 100: \( 0.4328 \times 100 = 43.28\% \).

Answer:

43.28%