Assume a box contains 2 red balls and 2 black balls. One black ball has been drawn and not replaced. What is the probability that in the next three draws there are two consecutive red balls?

Assume a box contains 2 red balls and 2 black balls. One black ball has been drawn and not replaced. What is the probability that in the next three draws there are two consecutive red balls?

• A. 1/3
• B. 2/3
• C. 1
• D. 0

Answer: (B)

After removing one black ball, the remaining balls are two red and one black. You’ll draw all three without replacement, so every order of these three balls is equally likely. The possible orders are red-red-black, red-black-red, and black-red-red. In two of these orders the two red balls appear consecutively (either at the start or at the end). Only one order has the red balls separated by the black ball. So the chance of two consecutive reds is 2 out of 3, which is 2/3.

After removing one black ball, the remaining balls are two red and one black. You’ll draw all three without replacement, so every order of these three balls is equally likely. The possible orders are red-red-black, red-black-red, and black-red-red. In two of these orders the two red balls appear consecutively (either at the start or at the end). Only one order has the red balls separated by the black ball. So the chance of two consecutive reds is 2 out of 3, which is 2/3.