Mathematical Enigma - XVI

Probability Level 3

Marie is getting married tomorrow, at an outdoor ceremony in the desert. In recent years, it has rained only 5 days each year.

Unfortunately, the weatherman has predicted rain for tomorrow. When it actually rains, the weatherman correctly forecasts rain 90 of the time. When it doesn't rain, he incorrectly forecasts rain 10 of the time.

What is the probability that it will rain on the day of Marie's wedding?

Give your answer to 3 decimal places.

The answer is 0.111.

1 solution

展豪張
Nov 25, 2015

Here I assume that 90 means 90%, 10 means 10% and there are 365 days each year.
For each year:
Predicted rain and it actually rains $=5\times 90\%=4.5$ days
Predicted rain and it does not rain $=360\times 10\%=36$ days
Probability that it rains if predicted rain $=\frac{4.5}{4.5+36}=\frac 1 9=0.111...$

Mathematical Enigma - XVI

The answer is 0.111.

1 solution

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