# What is an example of the law of large numbers?

##### 1 Answer

**Example 1:**

Suppose the population within a certain area is such that there are 3,497,419 females and 2,812,822 males (for a total population of 6,310,241)

If a random sample of 12 jurors is selected from this region, how many of the jurors will be women?

For an individual case, the answer could be anywhere from 0 to 12.

The law of large numbers says that if this process is repeated many **times** the **average** will be

**Example 2:**

A casino runs a wheel with numbers from 0 to 20.

A player pays $1 to play for each spin and gets $2 back if the wheel comes up with an odd number.

Since there are 11 odd numbers, the casino could be expected to win 11 out of 21 times (roughly 52.4% of the time).

With these values in mind a simulation was run with varying numbers of "spins" with the following results:

**number of spins** **casino wins/losses**

1

10

100

1000

10000

100000

While in the short run (note the example with 10 spins), the casino might lose, in the long run profitability is guaranteed.