Question

A local courier service sends packages to Toronto and offers a money back guarantee that each package will be delivered within 24 hours. The courier service sends 70% of packages by airplane, 20% by train, and 10% by van. If a package is sent by airplane, the probability it is delivered within 24 hours is 0.95. For packages sent by train and van, the probabilities they are delivered within 24 hours are 0.88 and 0.82, respectively. (a) Explicitly define the four basic events related to this question. In each subsequent part of this question, you must first express each probability in terms of these events and justify any computation through the use of a formula. (b) What proportion of the time will the courier service meet its guaranteed delivery time? (c) If a package fails to reach Toronto within 24 hours, what is the probability it was sent by train?

Answer 1