The weather forecast says the probability of it being cloudy tomorrow is 30%, the probability of it being rainy is 15%, and the probability of being cloudy and rainy is 14%. what is the probability of it being cloudy, if you it will be rainy?

a. about 21.43%

b. 46.67%

c. 4.5%

d. 93.3%

Step-by-step explanation:

This is a problem of conditional probability.

Let events

C=cloudy, P (C) = 0.30

R=rainy., P (R) = 0.15

C&R=cloudy and rainy, P (C&R) = 0.14

We are asked the probability of being cloudy given that it will be rainy

P (C|R) = P (C&R) / P (R) = 0.14/0.15 = 14/15 = 0.933 (to the thousandth)