Question 3

Ann is the owner of Pizzas R Us, a small company that delivers pizza from two different locations. The Mayfair site handles 30% of the total orders while the Claymont location delivers the remaining orders. In its promotional materials, Pizzas R Us strives to deliver all orders within 45 minutes. Historically, the Claymont location has experienced 5% of its orders taking longer than 45 minutes to deliver. The Mayfair store has been late on 8% of its orders.

Let’s define as “on-time” orders delivered within the 45 minutes, and as “late”, otherwise.

1. Provide the appropriate probabilities for the following expressions:

P(Claymont) =

P(on-time|Claymont) =

P(late|Claymont) =

P(Mayfair) =

P(on-time|Mayfair) =

P(late|Mayfair) =

2. Calculate the following joint probabilities:

P(late AND Claymont) =

P(late AND Mayfair) =

3. Calculate the probability of “late” using the law of total probability.

P(late) =

4. Ann has just spoken to a customer whose order was delivered 1 hour after it was placed but did not remember which location the order originated. What is the probability that the late order came from the Mayfair store?