Question

If there is a 90% chance of rain tomorrow and a 70% chance of wind and rain, what is the probability that it is windy, given that it is rainy? Round your answer to the nearest percent.

A.78% B.71% C.33% D.67%

Answer 1

R = event that it rains tomorrow
W = event that it is windy tomorrow
P(R) = probability of rain tomorrow = 0.90
P(W and R) = probability it is rainy and windy tomorrow = 0.70

Using the conditional probability formula, we can say
P(W|R) = probability it is windy, given it is rainy
P(W|R) = P(W and R)/P(R)
P(W|R) = 0.70/0.90
P(W|R) = 0.77778 <--- this is approximate
P(W|R) = 0.78 <--- rounding to two decimal places

Convert 0.78 to percent form and we get 78%

Answer: Choice A) 78%