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GRE 15- On average, a sharpshooter hits the target once in every 3 shots.

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On average, a sharpshooter hits the target once in every 3 shots. What is the probability that he will
not hit the target until the 4th shot?
(A) 1
(B) 8/81
(C) 16/81
(D) 65/81
(E) 71/81

The sharpshooter hits the target once in every 3 shots. Hence, the probability of hitting the target is 1/3. The
probability of not hitting the target is 1 – 1/3 = 2/3.
He will not hit the target on the first, second, and third shots, but he will hit it on the fourth shot. The
probability of this is
2/3.2/3.2/3.1/3=8/81
The answer is (B).

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