To find the probability that the second drawn ball is white, we need to consider the different possibilities of the first ball being black or white.

Let's break down the problem step by step:

Step 1: Total number of balls
There are a total of 3 black balls and 4 white balls in the bag, so the total number of balls is 3 + 4 = 7.

Step 2: Probability of drawing a white ball on the first draw
The probability of drawing a white ball on the first draw can be calculated by dividing the number of white balls by the total number of balls:
P(white on first draw) = 4/7

Step 3: Probability of drawing a black ball on the first draw
Similarly, the probability of drawing a black ball on the first draw can be calculated by dividing the number of black balls by the total number of balls:
P(black on first draw) = 3/7

Step 4: Probability of drawing a white ball on the second draw
Now, let's consider the different possibilities:
- If the first ball drawn is white, there will be 3 black balls and 3 white balls left in the bag. So, the probability of drawing a white ball on the second draw, given that the first ball was white, is:
P(white on second draw | white on first draw) = 3/6 = 1/2
- If the first ball drawn is black, there will be 4 white balls and 3 black balls left in the bag. So, the probability of drawing a white ball on the second draw, given that the first ball was black, is:
P(white on second draw | black on first draw) = 4/6 = 2/3

Step 5: Total probability of drawing a white ball on the second draw
To find the total probability of drawing a white ball on the second draw, we need to consider the probabilities of the different possibilities:
P(white on second draw) = P(white on second draw | white on first draw) * P(white on first draw) + P(white on second draw | black on first draw) * P(black on first draw)
= (1/2) * (4/7) + (2/3) * (3/7)
= 2/7 + 2/7
= 4/7

Therefore, the probability that the second drawn ball is white is 4/7 (option A).

B