To find P(A | B), we first need to understand the concept of independent events. When two events A and B are independent, the occurrence of one does not affect the occurrence of the other. This leads us to a critical formula:
P(A | B) = P(A)
This means that the probability of A occurring given that B has occurred, which is P(A | B), is the same as the original probability of A. Since we are given that P(A) = 0.5, we can directly apply this:
P(A | B) = 0.5
So, when events A and B are independent and both have a probability of 0.5, the probability of A occurring, given that B has occurred, remains 0.5.