In the hope of having a dry outdoor wedding, John and Mary decide to get married

Question

In the hope of having a dry outdoor wedding, John and Mary decide to get married in the desert, where the average number of rainy days per year is 10. Unfortunately, the weather forecaster is predicting rain for tomorrow, the day of John and Marys wedding. Suppose that the weather forecaster is not perfectly accurate: If it rains the next day, 90% of the time the forecaster predicts rain. If it is dry the next day, 10% of the time the forecaster still (incorrectly) predicts rain. Given this information, what is the probability that it will rain during John and Marys wedding? [Hint: Use Bayes Theorem.]

Explanation / Answer

probabilty of rain P(R)=10/365

probabilty of no rain =P(Rc)=355/365

forecast predicting rain . given rain in next day =P(FR|R)=0.9

forecast predicting rain . given dry in next day =P(FR|Rc)=0.1

hence probabilty that forecast of Rain =P(FR)=P(R)*P(FR|R)+P(Rc)*=P(FR|Rc) =(10/365)*0.9+(355/365)*0.1

=0.121918

hence probabilty of rain, given it has been forecasted=P(R|FR) =P(R)*P(FR|R)/P(FR) =(10/365)*0.9/0.121918

=0.202247

please revert

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.