Final answer:
The conditional probability P(A|B) is found using the formula P(A|B) = P(A AND B) / P(B). After calculating P(A AND B) = 0.24, we find that P(A|B) = 0.3.
Step-by-step explanation:
You are asking how to find the conditional probability P(A|B), which is the probability of event A occurring given that event B has already occurred. Given that P(A) = 0.4, P(B) = 0.8, and P(B|A) = 0.6, we can use the definition of conditional probability and the formula for it: P(A|B) = P(A AND B) / P(B). To find P(A AND B), we use the given conditional probability P(B|A), which is the probability of B happening given A has happened: P(A AND B) = P(B|A) * P(A) = 0.6 * 0.4 = 0.24. Now, we can calculate P(A|B):
P(A|B) = P(A AND B) / P(B) = 0.24 / 0.8 = 0.3.
Therefore, the probability of event A occurring given that event B has already occurred is 0.3.