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The third great principle of probabilities is that the chance that two events will happen—the first neither including nor excluding the second—is not the stun of the chances that they will severally happen, but the pro-duct of those chances.

Thus suppose the chance that one thing will happen

Is 1/1000 that a second will happen is   and that a third

will happen is Then out of 1,000,000 persons, as to each of whom these chances are equally applicable, the first thing will happen to 1,000; and out of this 1,000, to each of whom the second chance is equally- applicable, the second thing will happen to 10; and out of these 10, to each of whom the third chance is equally- applicable, the third thing will happen to i. Therefore all these things will happen to one out of the original 1,000,000; and the chance that all these will happen to a particular

one of them is ,, ,lo ,,,;, .   This is equal to the several

chances multiplied together, i. e, to ; 1/1000X 1/100 X

1

i~ oi)

In a similar manner it may be proved generally that where eyents are not mutually inclusive or exclusive, the probability that two or more will happen is the product of the probability that each will separately happen,

So, the chance of incurring a claim within a year on a joint life insurance on two lives is the ehance that one X611 die plus the chance that the other will die, less the product of the two chances. Or it may be given as certainty, which is 1, less the chances that both will survive the year, which is the product of the chance that one will survive and the chance that the other will sur-

vive ; for, if both do not survive the year, one at least must have died within it.