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5.35 The "law of averages," or the "gambler's fallacy," is the oft-quoted belief that if random events have come out one way for a number of trials they are "due" to come out the other way on one of the next few trials. (For example, it is the [mistaken] belief that if a fair coin has come up heads on 18 out of the last 20 trials, it has a better than 50:50 chance of coming up tails on the next trial to balance things out.) The gambler's fallacy is just that, a fallacy— coins have an even worse memory of their past performance than I do. Ann Watkins, in the spring 1995 edition of Chance magazine, reported a number of instances of people operat- ing as if the "law of averages" were true. One of the examples that Watkins gave was a letter to Dear Abby in which the writer complained that she and her husband had just had their eighth child and eighth girl. She criticized fate and said that even her doctor had told her that the law of averages was in her favor 100 to 1. Watkins also cited another example in which the writer noted that fewer English than American men were fat, but the English must be fatter to keep the averages the same. And, finally, she quotes a really remarkable application of this (non-)law in reference to Marlon Brando: "Brando has had so many lovers, it would only be surprising if they were all of one gender; the law of averages alone would make him bisexual." (Los Angeles Times, September 18, 1994, "Book Reviews," p. 13) What is wrong with each of these examples? What underlying belief system would seem to lie behind such a law? How might you explain to the woman who wrote to Dear Abby that she really wasn't owed a boy to "make up" for all those girls?