Probability of Meeting
Two men, call them X and Y, wish to meet at a certain place on a certain day, but no earlier than noon and no later than 12:15 p.m. If necessary, X will wait 6 minutes for Y to arrive, while Y will wait 9 minutes for X to arrive, but neither can stay past 12:15 p.m. Express (as a percent) their chance of meeting.
The answer is 74.
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1 solution
Since there are many possibilities for X and Y to meet, we have to use geometry and calculate the area that coincide with their chance of meeting bounded by the possibility frontier. Here are the conditions: Meeting time is from 12 noon - 12:15 , no earlier, no later. X will wait for only 6 mins and Y ,9 mins; or 0<=X<=6 and 0<=Y<=9
Create a chart and plot. X -axis is X arrival times and Y axis is Y arrival time.
X arrivals time that corresponds to Y's successful arrival time (X----------Y) (12:00------ 12:00-12:06) (12:02-------12:00-12:08) (12:04--------12:00-12:10) (12:06---------12:00-12:12) (12:08---------12:00-12:14) (12:09----------12:00-12:15) (12:10---------12:01-12:15) (12:12----------12:03-12:15) (12:14----------12:05-12:15) (12:15----------12:06-12:15)
Now plot the region. Calculate the area bounded Y=X+6 and Y=X-9. The total sample space is 225. The area bounded is 333/2 Hence, the percentage chance of them metting is (333/2)/225 or 74%