Statistics

Manage Impatience with Probability

A tool for meeting your impatient friend

Image courtesy of Pixabay

The Problem

Suppose that you and your friend are meeting “around 12:30” at the train station, but you are both loose with your schedule, and also both impatient. You might get there at 12, or at 1, or sometime in between; and you’ll only wait 15 minutes to meet your friend, or until 1, whichever is sooner. Your friend has the same tolerance, give or take, and he is also never quite on time, so you estimate he will be there at 12:30 give or take 30 minutes.

What is the probability that you will meet? Should you bet on it? (Try for yourself!)

Solutions

Let’s model this with some mathematics.

Geometric Solution

First, you want your arrival times to be less than 15 minutes apart; or else whoever got there first will leave. Let’s denote the arrival times as x and y, so we see that we will only meet when

Next, we make probability space of arrival times, which can be drawn as a square, where the x and y coordinates are your respective arrival times.