Assume a box contains 2 red balls and 2 black balls. One black ball has been drawn and not replaced. If the sequence starts with red, what is the probability that it ends with red?

Assume a box contains 2 red balls and 2 black balls. One black ball has been drawn and not replaced. If the sequence starts with red, what is the probability that it ends with red?

• A. 1/2
• B. 1
• C. 2/3
• D. 0

Answer: (A)

Drawing without replacement changes what’s left in the box after each draw. After one black ball has already been drawn and not replaced, the box has 2 red and 1 black (three balls total). If the first draw in the sequence is red, that red is removed, leaving 1 red and 1 black for the second draw. From these two remaining balls, the chance of drawing red next is 1 out of 2, which is 1/2.

Drawing without replacement changes what’s left in the box after each draw. After one black ball has already been drawn and not replaced, the box has 2 red and 1 black (three balls total). If the first draw in the sequence is red, that red is removed, leaving 1 red and 1 black for the second draw. From these two remaining balls, the chance of drawing red next is 1 out of 2, which is 1/2.