Two persons agreed to meet at a certain place between 2 PM and 3 PM. Each person has to wait another one for 10 minutes and then leave. What is the probability of their meeting if everyone can arrive whenever during this hour?
Let’s set a coordinate system XOY, the axis X corresponds to the arrival time of person A, the axis Y – for the arrival time of person B.
The whole data set is a square with the side 1 (1 hour), and the set of "favorable" outcome is a hexagon inside this square, bounded by the lines |x–y|≤1/6 (10 minutes = 1/6 of an hour). It’s easier to calculate the square of this hexagon as the difference between the whole square and two triangles: 1*1 - 2*(1/2)*(5/6)*(5/6) = 11/36.