Carcass wrote:

A bag contains 3 white, 4 black, and 2 red marbles. Two marbles are drawn from the bag. If replacement is not allowed, what is the probability that the second marble drawn will be red?

A. \(\frac{1}{36}\)

B. \(\frac{1}{12}\)

C. \(\frac{7}{36}\)

D. \(\frac{2}{9}\)

E. \(\frac{7}{9}\)

If a red marble is selected first and a red marble is selected second, the probability is:

2/9 x 1/8 = 2/72

If a red marble is not selected first and a red marble is selected second, the probability is:

7/9 x 2/8 = 14/72

So the overall probability is 2/72 + 14/72 = 16/72 = 2/9.

Answer: D

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