Two people arrive at a restaurant independently. Their arrival times are random and uniformly distributed between 5pm and 6pm (no moment in this interval is any more likely for arrival than another). What is the probability that the two people arrive within 10 minutes of each other?

:confused: please help me out. Thanks

davidwebb2

This is an old chestnut.

Draw a 6 by 6 square graph and plot the arrival times of one person on the x-axis and the arrival times of the other person on the y-axis. Plot their arrival times when they are 10 minutes apart. For instance plot (0,10), (10,20), (20,30) and so on.

Then plot (10,0), (20,10), (30,20)...

Now, connect the dots and you have a diagonal through the center of the grid.

There are 11 squares colored in the graph out of 36.

Therefore, the probability is 11/36.