### Home > INT2 > Chapter 5 > Lesson 5.1.4 > Problem5-48

5-48.

A sandwich shop delivers lunches by bicycle to nearby office buildings. Unfortunately, sometimes the delivery is made later than promised. A delay can occur either because food preparation takes too long, or because the bicycle rider gets lost. Last month the food preparation took longer than expected or the rider got lost $11\%$ of the time. During the same month, the food preparation took longer than expected $18$ times and the bicycle rider got lost $12$ times. There were $200$ deliveries made during the month. For a randomly selected delivery last month, what is the probability that both the food preparation took too long and the rider got lost?

$\text{By the Addition Rule: }0.11=\frac{18}{200}+\frac{12}{200}-\text{P(long and lost)}$