Question #382
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?
Expert's answer
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.
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.
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