This is an old chestnut. Here is an easy way to go about it.1.) Two university students agree to meet for a studying session. They decide to meet at a coffee shop some time between 6PM and 7PM, but neither of them enjoy waiting. Thus, they agree to leave if they have waited for fifteen minutes, or at 7PM, whichever comes first.
If both students show up randomly between 6PM and 7PM, what is the probability they will meet?
Draw a square with the time 6:00 at the origin and 7:00 at the end of the x and y axes. Then, draw two lines through the region, y=x+15 and
y=x-15. The region where they meet will be the area between the two lines. Find the area of the region between the lines and divide it by the entire region area. Label the x-axis the 'arrival time of one friend' and the y-axis the 'arrival time of the other friend'.
We can do this easily by finding the area of the two regions where they do not meet and subtract from the total area.
The line y=x-15 intersects the x-axis at 6:15 and the line y=x+15 intersects the y-axis at 6:15.
So, the areas where they do not meet has area (45)(45) because they are two triangles and 60-15=45. The total area is (60)(60)
So, we have 3600-2025=1575
See what i am getting at?.