Question

On average Tempe, AZ gets rain 29 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 6% of the time that it doesn't rain. What is the probability it is going to rain tomorrow?

Answer 1

$Let~P~be~event~that~the~weather~app~is~predicting~rain~tomorrow.\\ C~be~event~that~it~actually~does~rain.\\ Therefore~P(C)=29/365,~P(C^c)=1-(29/365)=336/365\\ P(P|C)=0.90,~P(P|C^c)=0.06\\ Then~required~probability=P(P)=P(P|C)P(C)+P(P|C^c)P(C^c)\\ =(29/365)*0.90+(336/365)*0.06=0.1267$