In old gangster movies on TV, you often hear of "number runners" or the "numbers racket." This numbers game, which is still played today, involves betting $1 on the last three digits of the number of stocks sold on a particular day in the future as reported in The Wall Street Journal. If the payoff is $600, what is the expectation for this numbers game?

In old gangster movies on TV, you often hear of "number runners" or the "numbers racket." This numbers game, which is still played today, involves betting $1 on the last three digits of the number of stocks sold on a particular day in the future as reported in The Wall Street Journal. If the payoff is $600, what is the expectation for this numbers game?

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Description: In old gangster movies on TV, you often hear of "number runners" or the "numbers racket." This numbers game, which is still played today, involves betting $1 on the last three digits of the number of stocks sold on a particular day in the future as r

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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The numbers racket is a well‑entrenched illegal gambling operation in most large cities. One version works as follows: you choose one of the 1000 three‑digit numbers 000 to 999 and pay your local numbers runner a dollar to enter your bet. Each day, one three‑digit number is chosen at random and pays off $600. The law of large numbers tells us what happens in the long run. Like many games of chance, the numbers racket has outcomes that vary considerably—one three‑digit number wins $600 and all others win nothing—that gamblers never reach "the long run." Even after many bets, their average winnings may not be close to the mean. For the numbers racket, the mean payout for single bets is $0.60 (60cents) and the standard deviation of payouts is about $18.96. If Joe plays 350 days a year for 40 years, he makes 14,000 bets. Unlike Joe, the operators of the numbers racket can rely on the law of large numbers. It is said that the New York City mobster Casper Holstein took as many as 25,000 bets…
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