Calculate the probability of reaching the solar thresholdass

Calculate the probability of reaching the solar threshold.assume that the probability of a rainy day in a given location is 0.30. We are interested in calculating the probability of reaching some solar radiation threshold. The following information is avaiable to us :

a) probability of reaching the solar threshold given that it was a rainy day is 0.25

b.) the probability of reaching the solar threshold given that it was not raining is 0.50.

Calculate the probability of reaching the solar threshold.

Solution

Let

S = reaching solar threshold
R = rainy

Note that

P(S) = P(R) P(S|R) + P(not R) P(S|not R)

= 0.30(0.25) + (1-0.30)(0.50)

= 0.425 [answer]