Question

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% of
the time. What is the probability that it will rain on the day of Alice’ wedding?

Answer 1

There is a 10% chance that it will rain on the day of Alice's wedding.

• The probability that it will rain on the day of Alice's wedding is calculated by considering the probability that the weather person's forecast is correct (90%) and the probability that the forecast is incorrect (10%).
• The probability that the forecast is correct is calculated by multiplying the probability of rain (1.4%) by the probability that the forecast is correct given that it is raining (90%).
• The probability that the forecast is incorrect is calculated by multiplying the probability of no rain (98.6%) by the probability that the forecast is incorrect given that it is not raining (10%).
• The total probability of rain on the day of the wedding is the sum of these two probabilities, which is 10%.
• This means that there is a 10% chance that it will rain on the day of Alice's wedding.

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