Answer to Question #28833 in Discrete Mathematics for Vernetta Marcellin

Question

The probability that on any given day, Susan carries her umbrella is 0.62. The probability that it rains and Susan has her umbrella is 0.56. What is the probability that it rains given that Susan had her umbrella.

Answer 1

This problem is about conditional probability: what is the probability that it rains if a condition is satisfied (the condition is that Susan had her umbrella).
The formula to use is the formula of conditional probability:
P(A|B) = P(A and B) / P(B),
where P(A|B) is the probability of event A happening if condition B is satisfied,
P(A and B) -the probability of events A and B happening at the same time,
P(B) - the probability of condition B.
Thus in the terms of our problem A is "it rains" and B is "Susan has her umbrella".
Then P(A|B) = P(A and B) / P(B) = 0.56 / 0.62 = 0.903