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A Mariner's Chance

Probability puzzles require you to weigh all the possibilities and pick the most likely outcome.

 Puzzle ID: #17169 Fun: (2.36) Difficulty: (1.71) Category: Probability Submitted By: toast9897

An old wartime story describes a sailor who, during a pitched battle, put his head through the hole made in the side of his ship by an enemy shell. His theory was that the odds of another shell landing in exactly the same spot should be extremely low.
Was his reasoning correct?

No. The chance of an unlikely event happening twice is fairly low, but the sailor's safety can't be calculated just by looking at the random nature of another shot landing in that hole. First, the destination of a shell is not entirely random--the guns are being aimed, and gunners who succeed with one shot may try again in the same direction. Second, each time a random phenomenon occurs, the probability of the same thing happening again is exactly the same. So, even if the guns weren't being aimed, the spot is just as likely to be hit as any other.
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