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 the black ball appears in the middle position?

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 the black ball appears in the middle position?

• A. 1/3
• B. 2/3
• C. 1
• D. 0

Answer: (A)

After taking out one black ball, the box has three balls left: one black and two red. The next three draws will place these three balls in some order, and each of the three possible positions for the single black ball is equally likely. The middle position among these three draws is the second one, which corresponds to the third draw overall. Since there are three equally likely spots for the black ball, the chance it lands in the middle is 1/3.

After taking out one black ball, the box has three balls left: one black and two red. The next three draws will place these three balls in some order, and each of the three possible positions for the single black ball is equally likely. The middle position among these three draws is the second one, which corresponds to the third draw overall. Since there are three equally likely spots for the black ball, the chance it lands in the middle is 1/3.