Question

If there is an 80% chance of rain and a 50% 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.

Answer 1

If the total probability when given it is rainy is 80% and the windy probability among 80% is 50% the total probability is...

50% / 80% = 62.5% ≈ 63%

Answer 2

The conditional probability that it is windy, given that it is rainy is is 63%.

Explanation:

It is given that there is 80% chance of rain, that is P(A)=0.80

50%chance of wind and rain, that is P(A∩B)=0.50

Now, the conditional probability that it is windy, given that it is rainy is:

`P(B|A)=\frac{P(A{\cap}B)}{P(A)}`

`P(B|A)=(0.50)/(0.80)`

`P(B|A)=0.625`

Thus, the conditional probability that it is windy, given that it is rainy is is 63%.