Atelevision 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

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