the less a die is loaded, the more casts must be made before
it can be shown that a certain side tends to recur oftener than once in
six.

(3) The rule for calculating the probability of a dependent event is the
same as the above; for the concurrence of two independent events is
itself dependent upon each of them occurring. My meeting with both A and
B in the street is dependent on my walking there and on my meeting one
of them. Similarly, if A is sometimes a cause of B (though liable to be
frustrated), and B sometimes of C (C and B having no causes independent
of B and A respectively), the occurrence of C is dependent on that of B,
and that again on the occurrence of A. Hence we may state the rule: If
two events are dependent each on another, so that if one occur the
second may (or may not), and if the second a third; whilst the third
never occurs without the second, nor the second without the first; the
probability that if the first occur the third will, is found by
multiplying together the fractions expressing the probability that the
first is a mark of the second and the second of the third.

Upon this principle the value of hearsay evidence or tradition
deteriorates, and generally the cogency of any argument based upon the
combination of approximate generalisations dependent on one another or
"self-infirmative." If there are two witnesses, A and B, of whom A saw
an event, whilst B only heard A relate it (and is therefore dependent on
A), what credit is due to B's recital? Suppose the probability of each
man's being correct as to what he says he saw, or heard, is 3/4: then
(3/4 x 3/4 = 9/16) the probability that B's story is true is a little
more than 1/2. For if in 16 attestations A is wrong 4 times, B can only
be right in 3/4 of the remainder, or 9 times in 16. Again, if we have
the Approximate Generalisations, 'Most attempts to reduce wages are met
by strikes,' and 'Most strikes are successful,' and learn, on
statistical inquiry, that in every hundred attempts to reduce wages
there are 80 strikes, and that 70 p.c. of the strikes are successful,
then 56 p.c. of attempts to reduce wages are unsuccessful.

Of course this method of calculation cannot be quantitatively applied if
no statistics are obtainable, as in the testimony of witnesses; and even
if an average numerical value could be attached to the evidence of a
certain class of witnesses, it would be absurd to apply it to the
evidence of any particular memb