If there is a 30% chance of sun tomorrow and a 20% chance of wind and no sun, what is the probability that it is windy, given that it is not sunny? round your answer to the nearest percent.
a. 44%
b. 29%
c. 22%
d. 57%

B. 29%

Step-by-step explanation:

if there is a 30% chance of sun tomorrow and a 20% chance of wind and no sun.

what is the probability that it is windy, given that it is not sunny.

A: it is not sunny

P(A)=0.7    (since, chance of being sunny=30% then chance of not being sunny=70%)

B:it is windy

A∩B:it is windy and not sunny

P(A∩B)=0.2  (chance=20%)

B/A:it is windy given that it is not sunny

Baye's theorem states that:

P(A∩B)=P(B/A)×P(A)

0.2=P(B/A)×0.7

⇒ P(B/A)= 2/7=0.286

             ≈ 29%

Hence, probability that it is windy, given that it is not sunny is:

 B.  29%