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:
[tex]P(A|B) = \frac{P(A \cap B)}{P(B)}[/tex]
In which
P(A|B) is the probability of A happening given that B happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(B) is the probability of B happening.
In this problem, we have that:
[tex]P(A \cap B) = \frac{3}{8}, P(B) = \frac{5}{7}[/tex]
So
[tex]P(A|B) = \frac{P(A \cap B)}{P(B)} = \frac{\frac{3}{8}}{\frac{5}{7}} = 0.525[/tex]
52.5% probability that A occurs given B occurs
