270 NATURE OF CAPITAL AND INCOME [Cmar. XVI

a person who draws a card from the hat receiving the prize
is two to one; for of the three equally probable drawings,
two are blanks.
In general terms the odds in favor of one event as compared
 with another are said to be m to n when there are
m + n equally probable cases in which one or the other of
the two events may happen, and among these m + n cases
there are m cases such that the first event would happen,
and n cases such that the second event would happen.
The chance of the first event is then 737 and the chance of
the second is -»=. The m and the n cases are, it should
be noted, assumed to be mutually exclusive."
Probability is thus not merely an affair of pure mathematics,
 as is so often imagined. It is, first of all, a matter
of concrete human estimate. What are called the mathematics
 of probability apply only to arrays of equally probable
 combinations, and consist in calculating the number of
these which are favorable or unfavorable to a given event.
The mathematics of probability never establish a probability
 of itself, but always rest on some human estimate
of chances which are equal to start with. Like every other
branch of applied mathematics, it must depend on having
its raw material supplied from without. By mathematics
we seem to discover that the chance of throwing double
sixes with two dice is one in thirty-six. But this calculation
 rests on the hypothesis that, in some person’s estimation,
 each die is equally liable to fall on any one of
its six faces. Starting with this assumption, it is easy to
show that in throwing two dice there are thirty-six equally
1 Tt often happens that we cannot divide the fleld of probability
into separate cases all equally probable. In such a case the mind is
forced to make an estimate. For instance, the probability of an
event may be said to be one third against the field if the estimator’s
state of opinion toward the field is exactly similar to his state of
mind toward another field in which the division into three separate

combinations 4s possible and one of them favors the event in question.
 If the state of mind is similar but less definite, then the chance

is “ about ”’ one third but not definite.