Question

Each day, there is a 0.1 probability that Caitlyn will leave her umbrella at home. If she leaves her umbrella at home, the probability it will rain is 0.7. If she takes her umbrella with her, the probability that it will rain is 0.1. On a randomly selected day, it rains. What is the probability Catilyn left her umbrella at home?

Answer 1

Given,

P(No Umbrella) = 0.1

So P(Umbrella) = 1 - 0.1 = 0.9

P(Rain | No umbrella) = 0.7

P(Rain | Umbrella) = 0.1

Hence by Bayes' theorem:

P(No umbrella | Rain)

= 0.4375