1 Let R be the event that it is a rainy day and let U be the

1. Let R be the event that it is a rainy day and let U be the event that I brought my umbrella to the office. We know that P(R^c) = 19/20, P(U) = 3/40 and P(U | R) = 3/4. What is the probability that it is a rainy day if you see my umbrella in the office? Write your answer in the box provided and show any working below. [2 marks]

Solution

Solution:

Given , P(U/R) = 3/4

=> P(U AND R) / P(R) = 3/4

=>P(U AND R) = 3/4 * P(R)

=>P(U AND R) = 3/4 * (1-P(R^c)

=>P(U AND R) = 3/4 * (1-19/20)

=>P(U AND R) = 3/4 * 1/20 = 3/80

Now,

P(It is rainy day/ Umbrella at office)

=P(R/U)

=P(R AND U) / P(U)

=P(U AND R) / P(U)

= 3/80 * 3/40

= 9/3200

= 0.0028125 Answer