Assume a box contains 2 red balls and 2 black balls. One black ball has been drawn and not replaced. If the last of the next three draws is red, what is the probability that the first is red?

• A. 1/3
• B. 1/2
• C. 2/3
• D. 1

Answer: (B)

After removing one black ball, the box has two red and one black. We will draw all three without replacement, so the possible color orders are Red-Red-Black, Red-Black-Red, and Black-Red-Red, each with equal likelihood (1/3).

If the last draw is red, the remaining possible sequences are Red-Black-Red and Black-Red-Red. In these two scenarios, the first draw is red in only one of them (Red-Black-Red). Since both are equally likely, the probability that the first draw is red given that the last draw is red is 1/2.