Solution to: Miss the Mark

Each shot has a chance of ¹/₃ to be the best. This is because the result of a shot is not dependent on an earlier shot. The chance that the third shot is not the best shot is 1 minus the chance that the third shot is the best shot. Therefore, the answer is ²/₃.

You can also look at the possible outcomes. Call the three successive arrows A, B and C. We know that arrow B is further from the bull's-eye than arrow A, so after shooting arrow C the following three outcomes are possible:

For two of the three outcomes, arrow C is worse than arrow A.

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