A television station would like to measure the ability of its weather forecaster. Past data have been collected that indicate the following:
Probability of sunshine on sunny days is 0.8
Probability of sunshine on rainy days is 0.4
Probability of a sunny day is 0.6
Find the probability of
(I)sunshine
(II)sunny given that the forecaster has predicted sunshine
I) Let us denote the probability of sunshine on rainy days with P(sunshine_sunny), the probability of sunshine on rainy days with P(sunshine_rainy), the probability of sunny day with P(sunny).and the probability of sunshine with P(sunshine). So, we can write: P(sunshine_sunny)=0.8 P(sunshine_rainy)=0.4 P(sunny)=0.6 There will be sunshine if on a sunny day is sunshine and when on a rainy day is sunshine, so the probability is: P(sunshine) = P(sunshine_sunny)*P(sunny) + P(sunshine_rainy)*P(rainy) =0.8*0.6+0.4(1-0.6)=0.48+0.16=0.64 II)The probability of sunny given that the forecaster has predicted sunshine is: P(sunny)=0.6
