Question

James travels from Toronto to Calgary then Vancouver and finally to Prince George. There is a 5% chance that his luggage is left behind in Toronto. If it is not left behind in Toronto, there is a 7% chance that it is left behind in Calgary. If it not left behind in Toronto or Calgary, there is a 10% chance that it is left behind in Vancouver. What is the probability his luggage is lost?

Answer 1

Let A be the event that the luggage is left behind in Vancouver, B be the event it is left behind in Calgary and C be the event it is being left behind in Toronto.

We have, P(C) = 0.05 i.e. P() = 1 - 0.05 = 0.95,

P(B | ) = 0.07 i.e. P( | ) = 1 - 0.07 = 0.93 i.e. P() = 0.93 * P() = 0.93 * 0.95 = 0.8835

and P(A | ) = 0.10 i.e. P( | ) = 1 - 0.10 = 0.90 i.e. P() = 0.90 * P() = 0.90 * 0.8835 = 0.7952

Thus, the probability that the luggage is lost = 1 - The probability that the luggage is not lost = 1 - P() = 1 - 0.7952 = 0.2048 (Ans).