Question

In a experiment, the probability that event A occurs is 5/9, the probability that event B occurs is 5/7, and the probability that event A and B both occur is 3/8. What is the probability that A occurs given B occurs

Answer 1

Answer:

52.5% probability that A occurs given B occurs

Step-by-step explanation:

Suppose we have two events, A and B, the conditional probability formula is:

$P(A|B) = \frac{P(A \cap B)}{P(B)}$

In which

P(A|B) is the probability of A happening given that B happened.

$P(A \cap B)$ is the probability of both A and B happening.

P(B) is the probability of B happening.

In this problem, we have that:

$P(A \cap B) = \frac{3}{8}, P(B) = \frac{5}{7}$

So

$P(A|B) = \frac{P(A \cap B)}{P(B)} = \frac{\frac{3}{8}}{\frac{5}{7}} = 0.525$

52.5% probability that A occurs given B occurs