Grinstead and Snell's Introduction to Probability by Peter G. Doyle, Charles M. Grinstead, and J. Laurie Snell

By Peter G. Doyle, Charles M. Grinstead, and J. Laurie Snell

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By Peter G. Doyle, Charles M. Grinstead, and J. Laurie Snell

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Example text

Finally, the complement of A is the set A˜ = {x | x ∈ Ω and x ∈ A} . The reason that these constructions are important is that it is typically the case that complicated events described in English can be broken down into simpler events using these constructions. For example, if A is the event that “it will snow tomorrow and it will rain the next day,” B is the event that “it will snow tomorrow,” and C is the event that “it will rain two days from now,” then A is the intersection of the events B and C.

In modern uses martingale has several different meanings, all related to holding down, in addition to the gambling use. For example, it is a strap on a horse’s harness used to hold down the horse’s head, and also part of a sailing rig used to hold down the bowsprit. The Labouchere system described in Exercise 9 is named after Henry du Pre Labouchere (1831–1912), an English journalist and member of Parliament. Labouchere attributed the system to Condorcet. Condorcet (1743–1794) was a political leader during the time of the French revolution who was interested in applying probability theory to economics and politics.

William Feller indicated the possibilities of using computer simulations to illustrate basic concepts in probability in his book An Introduction to Probability Theory and Its Applications. In discussing the problem about the number of times in the lead in the game of “heads or tails” Feller writes: The results concerning fluctuations in coin tossing show that widely held beliefs about the law of large numbers are fallacious. These results are so amazing and so at variance with common intuition that even sophisticated colleagues doubted that coins 5 D.

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