Final answer:
P(A|B) is the probability of A given B. Given P(A AND B) = 1/6 and P(B) = 7/24, the calculation of P(A|B) is straightforward using the given formula, resulting in a conditional probability of 4/7.
Step-by-step explanation:
The student asked for the conditional probability P(A|B) given P(A AND B) = 1/6 and P(B) = 7/24. To find P(A|B), we use the formula P(A|B) = P(A AND B) / P(B), assuming P(B) > 0. Substituting the given values into this formula, we get P(A|B) = (1/6) / (7/24).
By simplifying the fraction, we get P(A|B) = (1/6) * (24/7) = 4/7. Therefore, the probability of A occurring given that B has already occurred is 4/7.