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Printjmc
counting and probability senior
Problem
John needs to catch a train. The train arrives randomly some time between 2:00 and 3:00, waits for 20 minutes, and then leaves. If John also arrives randomly between 2:00 and 3:00, what is the probability that the train will be there when John arrives?
Solution
We put the time the train arrives on the -axis and the time John arrives on the -axis, and shade in the region where John arrives while the train is there.
The probability that John arrives while the train is at the station is the ratio of the shaded area to the whole square. If we divide the axes into 60 units, the shaded region can be split up into a triangle of area square units and a parallelogram of area square units, and the whole square has an area of 3600 square units. The ratio is .
The probability that John arrives while the train is at the station is the ratio of the shaded area to the whole square. If we divide the axes into 60 units, the shaded region can be split up into a triangle of area square units and a parallelogram of area square units, and the whole square has an area of 3600 square units. The ratio is .
Final answer
\frac{5}{18}