Guest Post by Willis Eschenbach
OK, quick gambler’s question. Suppose I flip seven coins in the air at once and they all seven come up heads. Are the coins loaded?
Near as I can tell, statistics was invented by gamblers to answer this type of question. The seven coins are independent events. If they are not loaded the chances of a heads is fifty percent. The odds of seven heads is the product of the individual odds, or one-half to the seventh power. This is 1/128, less than 1%, less than one chance in a hundred that this is just a random result. Possible but not very likely. As a man who is not adverse to a wager, I’d say it’s a pretty good bet the coins were loaded.
However, suppose we take the same seven coins, and we flip all seven of them not once, but ten times. Now what…
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