A box contains 7 white balls and 5 black balls. Two balls are drawn without replacement. What is the probability that both balls are white?

Step 1: Find the probability that the first ball is white.

There are 7 white balls out of 12 total balls.

P(first white) = 7/12

Step 2: Update the counts after a white ball is selected.

Because the ball is not replaced, there are now:
6 white balls remaining
11 total balls remaining

Therefore:
P(second white | first white) = 6/11

Step 3: Multiply the conditional probabilities.

P(both white) = (7/12)(6/11)

Step 4: Multiply the numerators and denominators.

P(both white) = 42/132

Step 5: Simplify the fraction.

42/132 = 7/22

As a decimal:
7/22 ≈ 0.3182

Therefore, the probability that both balls are white is 7/22, or approximately 0.3182.