Question

In an experiment, the probability that event B occurs is 1 /7 , and the probability that event A occurs given that event B occurs is 2/ 5 . What is the probability that events A and B both occur?

Answer 1

The probability that events A and B both occur is found by multiplying the probability of event B occurring, which is 1/7, by the probability of event A occurring given that B has occurred, which is 2/5. This gives us 2/35.

Step-by-step explanation:

To find the probability that events A and B both occur, we can use the formula P(A|B) = P(A AND B) / P(B). Given that P(B) = 1/7 and P(A|B) = 2/5, we can substitute these values into the formula to solve for P(A AND B). Solving for P(A AND B), we have P(A AND B) = P(A|B) * P(B) = (2/5) * (1/7) = 2/35. Therefore, the probability that events A and B both occur is 2/35.