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If there is a 10% 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.

A57%
B22%
C44%
D29%

Verified Answer :

W0lf93

Since there are two events happening simultaneously (windy and no sun), we can apply the concept of conditional probability here.

P(A|B) = P(A∩B)/P(B)

where it means that given B is happening, the probability that A is happening as well is the ratio of the chance for A and B to happen simultaneously over the chance of B to happen.

For our case, this can be interpreted as

P(A|B): it is the probability that it is windy (A) GIVEN that there is no sun (B)
P(A∩B) : chance of wind and no sun
P(B) : chance that there is no sun tomorrow

The chance of P(A∩B) is already given as 20% or 0.20. Since there is 10% or 0.10 chance of sun, then chances of having no sun tomorrow is (1-0.10) = 0.90.

Thus, we have P(A|B) = 0.2/0.9 ≈ 0.22 or 22%.

So, answer is B: 22%.

axesaber

22% is the correct answer so its B

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