Respuesta :
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,
[tex]P(B|A)=\frac{P(A\cap B)}{P(A)}[/tex]
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:
[tex]P(W|R)=\frac{P(W\cap R)}{P(R)}=\frac{0.10}{0.80}=0.125\approx0.13[/tex]
Thus, the probability that it is windy, given that it is rainy is 0.13.
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 = [tex]P(W \bigcap R)[/tex] = 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 = [tex]\frac{P(A \bigcap B)}{P(B)}[/tex]
So, P(W/R) = [tex]\frac{P(W \bigcap R)}{P(R)}[/tex] = [tex]\frac{0.10}{0.80}[/tex] = 0.125 or 12.5%
Therefore, probability that it is windy, given that it is rainy is 12.5% .
