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

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

• A. 0
• B. 1/3
• C. 1
• D. 2/3

Answer: (C)

After removing one black ball, the urn has 2 red and 1 black left. If the first of the next three draws is black, that black ball is taken out, leaving only red balls. With two red balls remaining and no black balls left, the next two draws must both be red with certainty. So the probability is 1.

After removing one black ball, the urn has 2 red and 1 black left. If the first of the next three draws is black, that black ball is taken out, leaving only red balls. With two red balls remaining and no black balls left, the next two draws must both be red with certainty. So the probability is 1.