Assume a box contains 2 red balls and 2 black balls. One black ball has been drawn and not replaced. If X2 and X3 are red, what is the probability that X1 is red?

Assume a box contains 2 red balls and 2 black balls. One black ball has been drawn and not replaced. If X2 and X3 are red, what is the probability that X1 is red?

• A. 0
• B. 1
• C. 1/2
• D. 1/3

Answer: (A)

With only two red balls in the urn, seeing red on both the second and third draws means those two red balls have already been taken by the time you reach X3. Since there are no red balls left, the first draw cannot be red. Therefore, the probability that X1 is red given that X2 and X3 are red is 0.

With only two red balls in the urn, seeing red on both the second and third draws means those two red balls have already been taken by the time you reach X3. Since there are no red balls left, the first draw cannot be red. Therefore, the probability that X1 is red given that X2 and X3 are red is 0.