heads and tails, respectively. If we toss
the coin many, many times, the result
should be close to 0.5. Of course, this
means that if we bet on the chances of
heads and tails, we will not be much of a
winner if we play too many games—and
we will have to have really good luck to
win if we play fewer games.
Chuck-a-luck is a gambling game
that has been played at many carnivals
over the years. It involves a player who
may bet on any one of the numbers 1
through 6, based on three dice placed in a
cage. If a selected number appears, the
gambler gets paid even money; if one of
the numbers comes up twice, the gam-
bler gets paid 2-1; and if the desired num-
ber comes up three times, the gambler
gets paid 3-1. But if the player worked it out, he or she would find that the game’s
expected odds are worse than for almost any other table game of chance. The game is
sometimes used as a fundraiser for charity, but the odds of coming away with more
money than originally put in are quite small. And they are even worse if someone has
loaded the dice.
Probability can also be associated with the violent “game” of chance called Russ-
ian roulette.In this bizarre sport, one or more of the six chambers of a revolver are
filled with bullets, the magazine is rotated at random, and the gun is fired at the play-
er’s head. The risk taker “bets” on whether or not the chamber that rotates into place
will be loaded. If it is, he loses not only his bet but also his life. Not to be outdone,
there are people who have come up with a modified version of Russian roulette. In this
case, the gun is loaded with a single bullet and two duelists alternately spin the cham-
ber. Each duelist fires at the other until one is killed; the probability of the first duelist
being killed is 6/11.
STATISTICS
What is statistics?
The analysis of events governed by probability is called statistics. In statistics, a group
of facts is collected and classified in a methodical manner, which is why such a study is
important to the fields of science, finance, social research, insurance, engineering,
and sundry other areas. In general, the data are grouped according to their relative 255
APPLIED MATHEMATICS
Games such as coin tossing and dice rolling are
common examples of the rules of probability in
action. Stone/Getty Images.