Assume a box contains 2 red balls and 2 black balls. One black ball has been drawn and not replaced. Without any additional information, what is the probability that the black ball is drawn before both red balls in the next three draws?

Assume a box contains 2 red balls and 2 black balls. One black ball has been drawn and not replaced. Without any additional information, what is the probability that the black ball is drawn before both red balls in the next three draws?

• A. 1/3
• B. 1/2
• C. 2/3
• D. 1

Answer: (A)

Think about drawing without replacement. After the initial black ball is taken out, the box has two red and one black. To have the black ball appear before both red balls in the next three draws, it must be drawn first among those three. The black ball’s position in the next three draws is equally likely to be first, second, or third. So the chance it’s first is 1 out of 3, i.e., 1/3.

Think about drawing without replacement. After the initial black ball is taken out, the box has two red and one black. To have the black ball appear before both red balls in the next three draws, it must be drawn first among those three. The black ball’s position in the next three draws is equally likely to be first, second, or third. So the chance it’s first is 1 out of 3, i.e., 1/3.