The Lottery Commission's intent seems pretty obvious: Encourage more gambling by Nebraskans, in spite of the fact that the law of probabilities makes it less likely that a record-breaking Powerball payoff will strike in Nebraska again.Write an explanation for what the Law of Large Numbers actually does say, and why there is no "law of probabilities" which makes it less likely that a record-breaking Powerball payoff will strike in Nebraska again, that in fact the chance that a large payoff occurs in Nebraska is not affected by whether or not there was such a payoff recently.

(What the Law of Large Numbers says is that if you repeat an experiment a lot of times the experimental percentage of the time that a certain outcome happens will be close to its actual probability to happen. For example, if you flip a fair coin many times, it will on average come up heads about half the time. Even if it came up heads 20 times in a row, after 1000 tosses those 20 heads probably will not make the average deviate much from 50%. For example, if it came up heads about half of the other 980 times, say 500 of those 980 times, then it came up heads 520 out of 1000 times for an experimental probability of 52%. If you then continued tossing it until you had done it 10,000 times and if it came up heads 4500 times over the extra 9000 tosses, the experimental probability would be (520+4500)/10000 = 5020/10000 = 50.2%. The probability gets close to 50%. But the coin did not come up tails less often for the last 9000 flips to make up for being heads too often for the first 1000 flips. If it just tends to come up heads about 50% of the time, then with enough flips any occasional excess gets averaged out.)

Here is a link to the relevant part of Andersen's column.