A probability problem

Question

A and B agree to meet at Queen’s College tomorrow.

They shall come at any time between 12:00 noon to 1:00 pm.

Each of them will wait for 15 minutes only.

They will immediately leave after 15 minutes or after 1:00 pm, whichever is earlier.

What is the probability that they can meet one another ?

Solution

The method of solving this problem is to apply the concept of Cartesian Coordinate system.

The x-axis shows the time after 12:00 in which A comes to school.

The y-axis shows the time after 12:00 in which B comes to school.

The area in blue shows that A comes too late and cannot meet B.

The area in green shows that B comes too late and cannot meet A.

The area in red shows that A can meet B.

You can find any point within these areas and study what happens.

Probability that they can meet one another

= (area in red) / (total area)

Lesson

Use one field of knowledge (co-ordinate geometry) to solve problem in another field (probability). This is common in Mathematics and other subjects.