Alice and Bob need to discuss a business project for 5 minutes. However, they haven't coordinated when they are going to be in the office, and in fact they are going to follow strict schedules of being in the office for only 15 minutes each. Each will arrive at an independently chosen random time between 2 PM and 3 PM, and their 5 minute discussion must end by 3 PM.

Given the randomness and lack of coordination, what is the probability that Alice and Bob will get to complete their 5-minute discussion?

Graphic solution:

Draw a 12*12 square, only 11*11 is relevant, i.e. 121 sq.unit,deduct 2 right triangles 2*1/2*9*9=81; that leaves 40/144 chances to meet

**40/144=5/18=27.78%**