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?
Solution
Problem
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 โ 0.3182
Therefore, the probability that both balls are white is 7/22, or approximately 0.3182.
Result
7/22 โ 0.3182