For two events and, the probability that occurs is 0.8, the probability that occurs is 0.4, and the probability that both occurs is 0.2. Given that occurred, what is the probability that also occurred?

P (B|A) = 0.25, P (A|B) = 0.5

Step-by-step explanation:

The question provides the following dа ta:

P (A) = 0.8

P (B) = 0.4

P (A∩B) = 0.2

Since the question does not mention which of the conditional probabilities need to be found out, I will show the working to calculate both of them.

To calculate the probability that event B will occur given that A has already occurred (P (B|A) is read as the probability of event B given A) can be calculated as:

P (B|A) = P (A∩B) / P (A)

= (0.2) / (0.8)

P (B|A) = 0.25

To calculate the probability that event A will occur given that B has already occurred (P (A|B) is read as the probability of event A given B) can be calculated as:

P (A|B) = P (A∩B) / P (B)

= (0.2) / (0.4)

P (A|B) = 0.5