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 first draw among the next three is red?

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 first draw among the next three is red?

• A. 2/3
• B. 1/3
• C. 1
• D. 0

Answer: (A)

After removing one black ball, the box has 2 red and 1 black, a total of 3 balls. The first draw among the next three will come from this 3-ball mix, so the probability of red is 2 out of 3, or 2/3. The fact that there will be two more draws afterward doesn’t change the chance of the very next draw, since it’s determined solely by the current composition.

After removing one black ball, the box has 2 red and 1 black, a total of 3 balls. The first draw among the next three will come from this 3-ball mix, so the probability of red is 2 out of 3, or 2/3. The fact that there will be two more draws afterward doesn’t change the chance of the very next draw, since it’s determined solely by the current composition.