The manager of a TV station wanted to assess the accuracy of the station\'s weat
ID: 3201380 • Letter: T
Question
The manager of a TV station wanted to assess the accuracy of the station's weather forecaster. On days that it rained the forecaster had correctly predicted rain 80% of the lime. On days that were sunny, the weather forecaster had correctly predicted sunny conditions 90% of the time. In the area that the station serves, it rains 30% of the time and is sunny 70% of the time. a) The weather forecast for today is for rain. What is the probability it will actually rain? b) What is the overall probability the forecaster is correct? c) Are the events "forecast is for rain" and "it rains" independent? Why or why not?Explanation / Answer
P(forecast for today is rain) = P(rain)*P(correct prediction as rain) +P(sunny)*P(wrong prediction as rain)
= 0.3*0.8+0.7*0.1 = 0.31
Probabity that it wil actually rain when the forecast is that it rains
= P(actully rain and forecasts correcty)/P(forecast for today is rain
= 0.3*0.8/0.31 = 0.774
b)Probablity that forscast is correct
= P(rain)*P(correctlt forecasted as rain)+P(sunny)*P(correcty forecasted as suuny)
=03*0.8+0.7*0.9 = 0.87
c)No theyare not independent because if A and B are independent the P(A n B) = P(A)P(B)
P(forecast is rain) = 0.31
P(rain) = 0.3
Probabilty that forecast is rain and it rains = 0.3*0.8
P(A n B) = P(A)P(B) condition is not satisfied
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