Question

question
given that $p(b|a) = 0.84$ and $p(a) = 0.43$, what is $p(b \text{ and } a)$?
provide your answer below:

Explanation:

Step1: Recall conditional probability formula

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

Step2: Rearrange formula to solve for \( P(B \text{ AND } A) \)

Multiply both sides of the formula by \( P(A) \) to get \( P(B \text{ AND } A)=P(B|A)\times P(A) \).

Step3: Substitute given values

We know \( P(B|A) = 0.84 \) and \( P(A)=0.43 \), so substitute these values into the formula: \( P(B \text{ AND } A)=0.84\times0.43 \).

Step4: Calculate the product

\( 0.84\times0.43 = 0.3612 \).

Answer:

\( 0.3612 \)