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

The total probability when given it is rainy is 80%. Among them, the windy probability among 80% is 50%. So the total probability is 50%/80%=62.5%≈63%.

Answer 2

The probability that it is windy, given that it is rainy is:

62.5%≈63%

Explanation:

Let A denote the event that it will rain.

B denote the event that it is windy.

A∩B denote the event that it is rainy and windy.

Let P denote the probability of an event.

i.e. we have:

P(A)=0.80

( Since there are 80% chance of rain)

P(A∩B)=0.50

(Since there are 50% chance of wind and rain)

We are asked to find:

P(B|A)

We know that:

`P(B|A)=(P(A\bigcap B))/(P(A))\\\\\\P(B|A)=(0.50)/(0.80)\\\\\\P(B|A)=0.625`

Hence, the probability in percent is:

62.5%≈63%