Question

In an experiment, the probability that event B occurs is 1 8 , and the probability that event A occurs given that event B occurs is 8 9 . What is the probability that events A and B both occur? Simplify any fractions.

Answer 1

The probability that events A and B both occur is 1/9.

To find the probability that events A and B both occur, we need to calculate the intersection of the events A and B. The formula for the conditional probability of A given B is P(A|B) = P(A AND B) / P(B).

Given that P(A|B) = 8/9 and P(B) = 1/8, we can plug these values into the formula to find P(A AND B). Solving for P(A AND B), we get:

P(A AND B) = P(A|B) * P(B)

= (8/9) * (1/8)

= 8/72

= 1/9