collected, or were different at some time
previous to the collection of evidence, every probable inference based
on those statistics must be corrected by allowing for the altered
conditions, whether we desire to reason forwards or backwards in time.

Sec. 7. The rules for the combination of probabilities are as follows:

(1) If two events or causes do not concur, the probability of one or the
other occurring is the sum of the separate probabilities. A die cannot
turn up both ace and six; but the probability in favour of each is 1/6:
therefore, the probability in favour of one or the other is 1/3. Death
can hardly occur from both burning and drowning: if 1 in 1000 is burned
and 2 in 1000 are drowned, the probability of being burned or drowned is
3/1000.

(2) If two events are independent, having neither connection nor
repugnance, the probability of their concurring is found by multiplying
together the separate probabilities of each occurring. If in walking
down a certain street I meet A once in four times, and B once in three
times, I ought (by mere chance) to meet both once in twelve times: for
in twelve occasions I meet B four times; but once in four I meet A.

This is a very important rule in scientific investigation, since it
enables us to detect the presence of causation. For if the coincidence
of two events is more or less frequent than it would be if they were
entirely independent, there is either connection or repugnance between
them. If, e.g., in walking down the street I meet both A and B oftener
than once in twelve times, they may be engaged in similar business,
calling them from their offices at about the same hour. If I meet them
both less often than once in twelve times, they may belong to the same
office, where one acts as a substitute for the other. Similarly, if in a
multitude of throws a die turns six oftener than once in six times, it
is not a fair one: that is, there is a cause favouring the turning of
six. If of 20,000 people 500 see apparitions and 100 have friends
murdered, the chance of any man having both experiences is 1/8000; but
if each lives on the average 300,000 hours, the chance of both events
occurring in the same hour is 1/2400000000. If the two events occur in
the same hour oftener than this, there is more than a chance
coincidence.

The more minute a cause of connection or repugnance between events, the
longer the series of trials or instances necessary to bring out its
influence: