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PART I
Law of Averages

Introduction | The Law of Large Numbers |
A general idea that many people hold goes something like this:

The longer a series of chance events goes on, the more likely it is that things will "even up." For example, the longer you drive a car, the more likely you are to have your share of flat tires. The more children you have, the more likely you will have an equal division of boys and girls (assuming an even number of children). The longer you flip a coin, the more likely the number of heads and tails will equalize.

Actually, the latter two examples are identical if certain simple assumptions are made. In the case of the coin, we shall suppose that the coin is "fair", so that on any one flip, head and tail are equally likely. In the case of the children, we shall rule out twins or other multiple births, and shall assume that the parents do not have any tendency to produce children of one sex as preferred to the other. Of course there is the practical consideration that one can flip a coin a lot more times than a woman can bear a child. So, it is more natural to use the coin for purposes of illustrating large samples. But for small samples, there is something unique about each child, which makes the family a marvelous illustration for stressing certain points.
 
 
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