Solution #21: Jaws

Let x be the percentage of a shark going undetected. We know that the probability of an alarm is 1/30. Hence the probability of having neither an undetected shark nor an alarm is
1 - (1/30 + x) = 29/30 - x
We have also been told that the probability of false alarm is 10x. Hence the probability of real alarm is 1/30 = 10x. But this is equal to 3x since 3 times as many sharks are detected as go undetected
1/30 - 10x = 3x
Hence x = 1/390

Thus the probability of a peaceful day is

29/30 - 1/390 = 0.964
Circle diagram
Source: Berrondom, Marie
Categories: Probability, Reasoning
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