MathProblem 38 Meeting at a restaurant problem

Two people arrive in a restaurant independently. Each arrives a random time between 5pm and 6pm, distributed uniformaly (no moment in this range is any more likely for arrival than another). What is the probability they arrived within 10 minutes of each other?

Solution

假设一个人到的时间为 \(x\)，另一个人为 \(y\)，则限制条件为

\[|x-y|\leq 10 \]

然后在坐标轴上面画出范围即可，那么概率即为两条线之间的面积比上总面积：

\[\frac{1100}{3600}=\frac{11}{36} \]