Question

On average Tempe, AZ gets rain 30.8 days a year (out of 365 days). Your weather app is predicting rain tomorrow. The app isn’t perfect though. It only predicts that it will rain around 90% of the time that it actually does rain, and it will predict rain about 9% of the time that it doesn’t rain. What is the probability that it is going to rain tomorrow?

Answer 1

Bayes' Theorem: P(A | B) = P(A & B) / P(B)

P(rain) = 30.8/365 = 0.0844

P(no rain) = 1 - 0.0844 = 0.9156

P(it is going to rain tomorrow | weather app is predicting rain tomorrow) = P(it is going to rain tomorrow and weather app is predicting rain tomorrow)/P(weather app is predicting rain tomorrow)

= P(it is going to rain tomorrow and weather app is predicting rain tomorrow) / [P(it is going to rain tomorrow and weather app is predicting rain tomorrow) + P(it is going to rain tomorrow and weather app is predicting rain tomorrow)]

= 0.0844x0.90/(0.0844x0.90 + 0.9156x0.09)

= 0.4797