Question

For the month of February in a certain​ city, 35​% of the days are cloudy. Also in the month of February in the same​ city, 24​% of the days are cloudy and rainy. What is the probability that a randomly selected day in February will be rainy if it is cloudy​?

Answer 1

Solution:

Let us define some events as follows:

A : A randomly selected day in February is cloudy

B : A randomly selected day in February is rainy

A ∩ B : A randomly selected day in February is cloudy and rainy

Since, 35% days are cloudy, therefore P(A) = 35/100 = 0.35

Since, 24% days are cloudy and rainy, therefore P(A ∩ B) = 24/100 = 0.24

We have to obtain the conditional probability of B given A i.e. we need to obtain P(B|A).

Conditional probability of B given A is given by,

We have, P(A) = 0.35

And since, P(B ∩ A) = P(A ∩ B) therefore, P(B ∩ A) = 0.24

Hence, the probability that a randomly selected day in February will be rainy if it is cloudy is 0.6857.

Please rate the answer. Thank you.