Final answer:
The probability that the first box was selected given that the marble is white can be found using conditional probability. The probability is 1/2.
Step-by-step explanation:
The probability that the first box was the one selected given that the marble is white can be determined using conditional probability. Let's denote A as the event that the first box was selected and B as the event that the marble is white. We want to find P(A|B), the probability of A given B.
Conditional probability can be calculated using the formula: P(A|B) = P(A ∩ B) / P(B).
In this case, P(A) is the probability of selecting the first box initially, which is 1/2 since there are two boxes. P(B) is the probability of selecting a white marble, which is also 1/2 since there are two white marbles out of four marbles in total in the first box.
P(A ∩ B) is the probability of selecting the first box and then selecting a white marble, which is (1/2) * (1/2) = 1/4.
Therefore, P(A|B) = (1/4) / (1/2) = 1/2.