Final answer:
To calculate P(A|B), we use the formula P(A|B) = P(A AND B) / P(B). By substituting the given values, P(A|B) is found to be 4/9, which corresponds to answer choice D.
Step-by-step explanation:
The general equation for conditional probability, represented as P(A|B), defines the probability of an event A occurring, given that another event B has already occurred. This concept is crucial in understanding how we calculate probabilities on a reduced sample space. To calculate P(A|B), we use the formula:
P(A|B) = P(A AND B) / P(B)
Given that P(AB) = 4/9 and P(B) = 1/3, we can substitute these values into the formula to find P(A|B):
P(A|B) = (4/9) / (1/3) = (4/9) * (3/1) = 4/3 * 1/3 = 4/9
Therefore, P(A|B) = 4/3, which simplifies to 4/9 after multiplying the fractions. Hence, the answer is D. 4/9.