Two friends decide to meet at a definite place between 9 AM and 10 AM. The first to arrive waits for his friend for 15 minutes and then leaves. If each of them arrives at an arbitrary moment between 9 and 10 AM, find the probability that they will meet.
We can treat this problem geometrically. The interval from 9:00 AM to 10:00 AM represents a segment of length 1. Let a unit length segment on the x axis represent one friend’s sample space. Let a unit segment on the y axis represent the other friend’s sample space. The total sample space is then an area of unit length squared. Every point in this unit square represents the arrivals of the two friends.
The events(x,y) during which the friends actually meet are given by the condition
The intersection of the above band with the unit square gives us the required probability (7/16)