The Sum of Draws

The sum of draws can be illustrated by the following process. Imagine there is a box of tickets, each having a number 1, 2, 3, 4, 5, or 6 written on it.

The sum of draws can be represented by a process in which tickets are drawn at random from the box, with the ticket being replaced to the box after each draw. Then, the numbers on these tickets are added up. By replacing the tickets after each draw, you are able to draw over and over under the same conditions.

Say you draw twice from the box at random with replacement. To find the sum of draws, you simply add the first number you drew to the second number you drew. For instance, if first you draw a 4 and second you draw a 6, your sum of draws would be $4+6=10$. You could also first draw a 4 and then draw 4 again. In this case your sum of draws would be $4+4=8$. Your sum of draws is, therefore, subject to a force known as chance variation.

This example can be seen in practical terms when imagining a turn of Monopoly. A player rolls a pair of dice, adds the two numbers on the die, and moves his or her piece that many squares. Rolling a die is the same as drawing a ticket from a box containing six options.

Sum of Draws In Practice

Rolling a die is the same as drawing a ticket from a box containing six options.

To better see the affects of chance variation, let us take 25 draws from the box. These draws result in the following values:

3 2 4 6 3 3 5 4 4 1 3 6 4 1 3 4 1 5 5 5 2 2 2 5 6

The sum of these 25 draws is 89. Obviously this sum would have been different had the draws been different.