Solution #22: Meteorology
There are four possible situations:
- Fair weather predicted and occurred: probability 1/2 * 2/3 = 1/3.
- Fair weather predicted but rain occurred: probability 1/5 * 1/3 = 1/15.
- Rain predicted and occurred: probability 4/5 * 1/3 = 4/15.
- Rain predicted but fair weather occurred: probability 1/2 * 2/3 = 1/3.
Let i be the measure of the inconvenience for Francine to carry her
umbrella around for one whole fine day and 2i the measure of
inconvenience of not having an umbrella when it rains. If she systematically
carries her umbrella every day, the inconvenience will amount to i on
two days out of three, hence an average inconvenience of 2i/3.
If she never takes her umbrella, the inconvenience will amount to 2i
one day out of three, for an average inconvenience again of 2i/3.
If she decides to follow the advice of the weather forecasters and takes her
umbrella only when rain is predicted why will suffer an inconvenience of
i on 1 day out of 3, and ii on 1 day out of 15, which amounts to
and average penalty of 7/i/15 (less than the two previous average
penalties). We recommend, therefore, that Francine follow the advice of the
weather forecasters.
Source: Berrondom, Marie
Categories: Probability, Reasoning
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