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Extra info for Chances are... IADVENTURES N PROBABILITY
But in real life, we may not have that information; all we have is the product of the multiplication: the number of things that actually happened. Poisson’s curve, more a steeple than a bell, plots this product of probability times number of trials for things that happen rarely but have many opportunities to happen. The classical case of a Poisson distribution, studied and presented by the Russian-Polish statistician Ladislaus Bortkiewicz, is the number of cavalry troopers kicked to death by horses in 14 corps of the German army between 1875 and 1894.
5 trials: exactly the answer Pascal got by calculating cases. Inﬁnite series and logarithms also gave de Moivre the key to under- 36 Chances Are . . standing Pascal’s Triangle—and, with it, the bell curve. A few pages ago we blithely said that if you wanted to know, say, the chance that a heads will appear in n tosses of a coin, you need only count n rows down the triangle and a across to ﬁnd the coefficient. Easy enough for ﬁve or six trials, but imagine actually doing it for a series of 1,000 trials.
Pascal says that, since we have no way of knowing God, we can assume equal probabilities of winning and losing, so p X ϭ 1/2. At these odds, you need to be offered only two lives to make the game fair; if three were offered, you’d be a fool not to bet on God’s side. ” Pascal was not so cynical; for him, the calculation genuinely expressed a belief that probability can offer a handle on the unknown, even if that unknown were as great as the question of our salvation. The Chevalier de Méré was not simply a high-living gamester but also a capable mathematician.