# Probability that 2 individuals see each various other at the coffee bar

2 mathematicians each entered into a coffee bar at an arbitrary time in between 8:00 a.m. and also 9:00 a.m. daily. Each orders a mug of coffee after that rests at a table, reviewing a paper for 20 mins prior to entrusting to most likely to function.

On any kind of day, what is the probability that both mathematicians go to the coffee bar at the very same time (that is, their arrival times are within 20 mins of each various other)?

Working in hrs and also allowing 8 :00 a.m. be t = 0, each mathematician's arrival time is a number in between 0 and also 1. The example room can be stood for by the device square in the coordinate aircraft with one teacher's arrival time as x and also the various other's as y, where areas with equivalent locations are just as most likely. We desire x - 1/ 3 < y < x+1/ 3 - - that is, the 2nd teacher gets here previously than the first by no greater than 1/ 3 of a hr or behind the first by no greater than 1/ 3 of a hr.

The location of the wanted area is 5/ 9.

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