The Law of Large Numbers means that as the number of observations of an outcome

Question

The Law of Large Numbers means that as the number of observations of an outcome of a trial becomes larger the running mean of the relative frequency of the outcome of interest appears to settle down to a constant value, the probability of the outcome. You have just flipped a fair coin 7 times getting all heads. Does the coin owe you a tai1? The Law of Averages predicts you are due for a tail, but it is a myth. So, if using the same fair coin, no because the probability of a head on the next toss hasn't changed. Is a good hitter in baseball who has struck out the last six times due for a hit his next time up?

Explanation / Answer

No.

Reason Because the law of large numbers says nothing about short-run behaviour. Relative frequencies even out only in the long run, and this long run is really long. The so called law of averages (that an outcome of a random event that hasnt occurred in many trials is "due" to occur) doesnt exist at at all.

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