1. Chance variables.
When a pair of dice are rolled, the total number of points that show
could be either 2, 3, … 11, or 12. When a coin is tossed 10 times, the
number of times a head comes up could be 0, 1, … 9, or 10. The total
number of points, and the number of times a head comes up, are
. In the Frst example, the numbers 2
through 12 are said to be the
of the total number of
points. In the second example, the numbers 0 through 10 are the pos-
sible values of the number of times heads comes up. People often drop
the “possible”, and just use “the values”.
In mathematics, entities that can have different values within the
same context are often referred to as variables. The total number
of points (when a pair of dice are rolled) is a variable because it is
possible for it to be any number between 2 and 12 inclusive. It is a
“chance” variable because the possible values have chances: the value
2 has chance 1/36, the value 3 has chance 2/36, and so on.
If a roulette player stakes $1 on red at roulette, two things can hap-
pen. Either he wins, in which case the casino returns his stake along
with another dollar as prize; or he loses, in which case the casino
keeps the stake.
A roulette player bets $1 on red six times in a row. His
the six bets is deFned as:
net gain = amount he wins — amount he loses
Net gain is a chance variable. What are its possible values?
What is the best that could happen to the gambler? He could win ev-
ery time. In that case his net gain would 6 (dollars). What is the worst
that could happen? He could lose every time, and the net gain would
be –6 (dollars). So the possible values are whole numbers between –6
and 6 (inclusive). But not all whole numbers. Suppose the gambler
wins Fve times and loses once. His net gain would be 4 (dollars). The
possible values of net gain are: –6, –4, –2, 0, 2, 4, 6.