Question

If there is an 80% chance of rain and a 10% 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

Answer:

The probability that it is windy, given that it is rainy is 0.13.

Step-by-step explanation:

The conditional probability of an event B given that another event A has already occurred is,

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

Denote the events as follows:

R = rainy weather

W = windy weather

Given:

P (R) = 0.80

P (W ∩ R) = 0.10

Compute the probability that it is windy, given that it is rainy as follows:

$P(W|R)=\frac{P(W\cap R)}{P(R)}=\frac{0.10}{0.80}=0.125\approx0.13$

Thus, the probability that it is windy, given that it is rainy is 0.13.

Answer 2

Answer:

Required Probability = 0.125 or 12.5%

Step-by-step explanation:

We are given that there is an 80% chance of rain and a 10% chance of wind and rain.

Let Probability of rain = P(R) = 0.80

and Probability of wind and rain = $P(W \bigcap R)$ = 0.10

We have to find the probability that it is windy, given that it is rainy i.e,; P(W/R)

Firstly, The conditional Probability P(A/B) is given by = $\frac{P(A \bigcap B)}{P(B)}$

So, P(W/R) =  $\frac{P(W \bigcap R)}{P(R)}$ = $\frac{0.10}{0.80}$ = 0.125 or 12.5%

Therefore, probability that it is windy, given that it is rainy is 12.5% .