Final answer:
To find the conditional probability P(A|B), we use the formula P(A|B) = P(A ∩ B) / P(B). With P(A ∩ B) = 0.2 and P(B) = 0.5, the calculation gives us P(A|B) = 0.4.
Step-by-step explanation:
The question is related to the concept of conditional probability in mathematics. Conditional probability, denoted as P(A|B), is the probability of event A occurring, given that event B has already occurred. The question provides that the probability of both events A and B occurring, P(A ∩ B), is 0.2 and the probability of event B occurring, P(B), is 0.5. To find the conditional probability of A given B, P(A|B), we will use the formula P(A|B) = P(A ∩ B) / P(B).
Given that P(A ∩ B) = 0.2 and P(B) = 0.5, we can calculate:
P(A|B) = P(A ∩ B) / P(B) = 0.2 / 0.5 = 0.4.
Therefore, the conditional probability of event A occurring given that event B has occurred is 0.4.