A box contains 5 red and 4 white marbles. Two marbles are drawn successively from the box without replacement and the second drawn marble is found to be white. Probability that the first is also white is?

A. 3/8
B. 1/2
C. 1/3
D. 1/4

To find the probability that the first marble drawn is white given that the second marble drawn is white, you can use conditional probability.

Let's denote the events as follows:
A = The first marble drawn is white.
B = The second marble drawn is white.

You want to find P(A|B), the probability that A occurs given that B has occurred.

You can use the formula for conditional probability:
P(A|B) = P(A and B) / P(B)

First, calculate P(B), the probability that the second marble drawn is white.

Since the first marble drawn is not replaced, there are now 8 marbles left in the box (4 white and 4 red). The probability of drawing a white marble on the second draw is 4/8 because there are 4 white marbles out of the total 8 marbles left.

Now, let's calculate P(A and B), the probability that both the first and second marbles drawn are white.

For the first draw, there are 4 white marbles out of a total of 9 marbles in the box. So, the probability of drawing a white marble on the first draw is 4/9.

Now, for the second draw, there are 3 white marbles left (since one was already drawn on the first draw), and there are a total of 8 marbles left. So, the probability of drawing a white marble on the second draw given that the first draw was white is 3/8.

To find P(A and B), you multiply the probabilities of both events:
P(A and B) = (4/9) * (3/8)

Now, you can calculate P(A|B) using the formula:
P(A|B) = P(A and B) / P(B) = [(4/9) * (3/8)] / (4/8) = (4/9) * (3/8) / (4/8) = (4/9) * (3/8) * (8/4) = (4/9) * (3/4) = 3/9 = 1/3

So, the probability that the first marble is white given that the second marble is white is 1/3.

Therefore, the correct answer is C. 1/3.