Alice is getting married on May 5th at an outdoor ceremony in a desert. In recent years it has rained only 5
days each year. Unfortunately the weather person has predicted rain for tomorrow. When it actually rains the
weather person correctly forecasts rain 90% of the time. When it doesn’t rain, he incorrectly forecasts rain 10%?
Answers
Given : Alice is getting married on May 5th at an outdoor ceremony in a desert. In recent years it has rained only 5 days each year.
weather person has predicted rain for Wedding day
When it actually rains the weather person correctly forecasts rain 90% of the time.
When it doesn’t rain, he incorrectly forecasts rain 10%
To Find : probability that it will rain on the day of Alice’ wedding?
Solution:
Rain 5 days in a year
Probability of Rain on any Day = 5/365 = 1/73
Rain Happens on wedding Day = (1/73)
weather person has predicted rain for tomorrow. When it actually rains the
weather person correctly forecasts rain 90% of the time.
= (1/73) (0.9)
= 0.9/73
Rain Does not Happens on wedding Day = 1 - (1/73) = 72/73
When it doesn’t rain, he incorrectly forecasts rain 10%?
= (72/73) (0.1)
= 7.2/73
Probability that Rain Happens on wedding Day = 0.9 / (0.9 + 7.2)
= 0.9/8.1
= 1/9
= 0.111
Probability that Rain Happens on wedding Day = 1/9 = 0.111
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