in an experiment, the probability that event b occurs is 2/9, and the probability that event a occurs given…

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|B) ) is the probability of ( A ) given ( B ), ( P(A \cap B) ) is the probability of both ( A ) and ( B ) occurring, and ( P(B) ) is the probability of ( B ) occurring.

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

Multiply both sides of the formula by ( P(B) ) to get ( P(A \cap B) = P(A|B) \times P(B) ).

Step3: Substitute the given values

We know that ( P(B) = \frac{2}{9} ) and ( P(A|B) = \frac{4}{7} ). Substituting these values into the formula, we get ( P(A \cap B) = \frac{4}{7} \times \frac{2}{9} ).

Step4: Multiply the fractions

To multiply the fractions, multiply the numerators together and the denominators together: ( \frac{4 \times 2}{7 \times 9} = \frac{8}{63} ).

Answer:

(\frac{8}{63})