the probability that it is raining is 25 the orbability that

the probability that it is raining is .25. the orbability that it is windy is .30. if it is windy, the probability that it is raining is .40. what is the probabilty that it is raining and windy? assume that the events raining and windy are not independent.

Solution

Let R denote the event of raining and W that of winding.

Given, P(R)=.25

P(W)=.3

and P(R|W) = .4

We know P(R|W) = P(RW) /P(W)

=> P(RW) = P(R|W)*P(W)

=>P(RW)=P(It is raining and windy)=(.4)*(.3)=0.12