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A man has a probability of 2/5 of hitting a target on a single shot. If he shoots at the target k times, where k is a given integer, what is the least value of k for which the probability of hitting the target at least once exceeds 7/10?
- 3
- 5
- 2
- 4
Correct answer: 3
Solution
P(at least one hit) = 1 - (3/5)^k > 7/10 means (3/5)^k < 3/10. For k=2, (3/5)^2 = 0.36 > 0.3; for k=3, 0.216 < 0.3. So the least k is 3.
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