This is a fairly classic problem...one of the solutions involves drawing a square of side length 1 on an xy-plane (say, with coordinates (0,0), (1,0), (1,1), (0,1)). We label the axes so that the x-axis corresponds to A's arrival time, and the y-axis corresponds to B's arrival time. Here, (0,0) corresponds to both A and B arriving at 10:00, (1/2, 1/2) corresponds to both A and B arriving at 10:30, and so on.

The probability that A and Bdomeet is given by a certain geometric region S. Find the area of S. The probability that they do not meet is simply 1-S.