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The weathermen are always wrong
The local weatherman says No Rain, and his record is 2/3 accuracy of
prediction. But the Federal Meteorological Service predicts rain, and
their record is 3/4.
With no other data available, what is the chance of rain?
Solution
Assuming the two sources are independent:
P(rain) = P(weatherman is wrong and FMS is right) = 1/3 * 3/4 = 1/4
P(no rain) = P(weatherman is right and FMS is wrong) = 2/3 * 1/4 = 1/6
Actual probability of rain = P(rain) / (P(rain) + P(no rain))
= (1/4) / (1/4 + 1/6) = 3/5.
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