# Demonstration of the law of large numbers

This macro simulates the tossing of a coin a specified number of times, and calculates the total number of tosses, the total number of heads, the proportion of heads, and the difference between the total number of heads and the total number of tails.

Be sure that Minitab knows where to find your downloaded macro. Choose Tools > Options > General. Under Macro location browse to the location where you save macro files.

###### Important

If you use an older web browser, when you click the Download button, the file may open in Quicktime, which shares the .mac file extension with Minitab macros. To save the macro, right-click the Download button and choose Save target as.

## Running the Macro

To run the macro, click anywhere in the Session window and choose Editor > Show Command Line. At the command prompt (MTB>), type the following:

`%COUNTHEM`

Press Enter.

When you are prompted, enter the number of times to toss the coin, and the number of sets to toss the coin that many times. For example, if you wish to toss the coin 50 times and repeat that 5 times for a total of 250 tosses, enter 50, 5 and press Enter.

Results of 100 tosses performed one time.

```ROW  NUMTOSS  NUMHEADS  PROPORTN   DIFF
1      100        52      0.52      4
```

You can see that 100 tosses yielded 52 heads.

Results of 100 tosses performed 10 times

```ROW  NUMTOSS  NUMHEADS   PROPORTN   DIFF
1      100        52   0.520000      4
2      200       101   0.505000      2
3      300       147   0.490000     -6
4      400       198   0.495000     -4
5      500       252   0.504000      4
6      600       294   0.490000    -12
7      700       347   0.495714     -6
8      800       396   0.495000     -8
9      900       454   0.504444      8
10     1000       509   0.509000     18
```

The proportion of heads appears to be approaching 0.5. The differences between the number of heads and the number of tails have varied widely.

Investigate with graphs

If you create a scatterplot of the proportion of heads (PROPORTN) against the number of tosses (NUMTOSS) you will notice that it is approaching 0.5.

If you create a scatterplot of the differences between the number of heads and the number of tails (DIFF)versus the number of tosses (NUMTOSS) you will notice something completely different.

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