Question

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%

Answer 1

It's B 29%

You know there's a 20% chance of wind and no sun.
And there must be a 70% chance of no sun. Since there's a 30% chance of sun
If you divide 0.20 / 0.70 you get .2857 which rounds to 29%.

Answer 2

B. 29%

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%