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