# Learn the Law of Large Numbers

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Transcript

In the main lesson, you learned that probability tells you the likelihood that an event will happen.

You simulated rolling the dice eleven times.

In this extension, you will see how the probability changes when you work with a larger sample size, such as 500 rolls.

You will learn the law of large numbers and use Google Sheets to test it out.

The law of large numbers says that the more times you perform the same experiment, the closer the actual results get to the predicted results.

The law of large numbers implies that the more times you roll the dice, the closer the actual results will come to the probability, or predicted results.

Update the title.

Your sheet shows the results for 11 rolls.

Compare the Probability column with the Actual Percentage rolled column.

Notice the differences between the predicted outcomes and the actual outcomes.

Now, see what happens when you roll the dice 500 times.

Hold down shift and select the bottom row of cells in the dice simulation columns.

Then, drag the cell handle to copy the RANDBETWEEN formulas to at least 500 more rows.

Scroll back up to the top of your sheet.

Copy the new values in the roll simulation columns.

And paste only the values in the number rolled columns.

Next, add the orange and purple dice together for the new rolls.

Copy the sum formula to at least row 502.

Now that you have simulated rolling each die 500 times and added the dice together, count how many times each outcome appeared.

First, change the title of the Number of Times column to indicate the new number of rolls.

Then, use the COUNTIF formula to calculate how many times each outcome appeared in the 500 rolls.

Update the range of the COUNTIF formula to include the new dice rolls.

The first two rows are headings, so the last row in the range is 502.

Copy the formula to the rest of the column.

Finally, change the percentage formula, since you rolled the dice 500 times instead of 11.

Change the number of rolls in the formula in the Actual Percentage Rolled column from 11 to 500.

Copy the formula to the rest of the column.

Compare the actual outcomes with the probable outcomes.

To make it easier to compare your results, hide the columns you don’t need.

After 500 rolls, the percentages of each actual outcome are closer to the probability you calculated than they were after 11 rolls.

You just demonstrated the Law of Large Numbers using Google Sheets!

Add 500 more dice rolls in the simulation columns, Copy and paste the new values to freeze the data, Copy the SUM formula to add the new dice rolls.

Update the range in the COUNTIF formula and the total number of dice rolls in the Actual Percentage formula.

And compare the actual outcomes to the probable outcomes.

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## Instructions

Choose an extension from the list to continue learning ways to use Google Sheets to perform calculations.