Let A and B be events in a sample space S such that P(A) = 0.6, P(B) = 0.4, and P(A B) = 0.27. Find the probabilities below
P(A|B)
To find the probability of event A given event B, denoted as P(A|B), we use the formula:
P(A|B) = P(A ∩ B) / P(B)
Given that P(A ∩ B) = 0.27 and P(B) = 0.4, we can substitute these values into the formula:
P(A|B) = 0.27 / 0.4
Simplifying,
P(A|B) = 0.675
Therefore, the probability of event A given event B is 0.675 or 67.5%.