Question

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.
A. 57%
B. 22%
C. 44%
D. 29%

Answer 1

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%.

Answer 2

22% is the correct answer so its B