Question

For the month of April in a certain city, 86% of the days are cloudy. Also in the month of April in the same city, 45% of the days are cloudy and rainy. What is the probability that a randomly selected day in April will be rainy if it is cloudy?The probability is approximately (Round to three decimal places as needed)

Answer 1

0.523

Step-by-step explanation:

Given;

Probability of cloudy days, P(cloudy days) = 86% = 86/100 = 0.86

Probability of rainy and cloudy days, P(rainy and cloudy days) = 45% = 0.45

So we can go ahead and determine the probability that a randomly selected day in April will be rainy if it is cloudy using the below formula;

`P(\text{ rainy if cloudly) }=\frac{P(cloudy\text{ and rainy)}}{P(\text{cloudy)}}`
`P(\text{ rainy if cloudly) }=(0.45)/(0.86)=0.523\text{ (to thre}e\text{ decimal places)}`

So the probability that a randomly selected day in April will be rainy if it is cloudy is 0.523