MathDB

Three friends are trying to meet for lunch at a cafe. Each friend will arrive independently at random between

1\!:\!00

pm and

2\!:\!00

pm. Each friend will only wait for

5

minutes by themselves before leaving. However, if another friend arrives within those

5

minutes, the pair will wait

15

minutes from the time the second friend arrives. If the probability that the three friends meet for lunch can be expressed in simplest form as

\tfrac{m}{n}

, what is

m+n

Problem Statement