A Philosophical Essay on ProbabilitiesLaplace, Pierre Simon, marquis de
Philosophy
A Philosophical Essay on Probabilities
Laplace, Pierre Simon, marquis de
Probabilities
The ratio of the population to annual births is then 28 + (352845/1000000);
it is greater than had been estimated up to this time. Multiplying the
number of annual births in France by this ratio, we shall have the
population of this kingdom. But what is the probability that the
population thus determined will not deviate from the true population
beyond a given limit? Resolving this problem and applying to its
solution the preceding data, I have found that, the number of annual
births in France being supposed to be 1000000, which brings the
population to 28352845 inhabitants, it is a bet of almost 300000 against
1 that the error of this result is not half a million.
The ratio of the births of boys to that of girls which the preceding
statement offers is that of 22 to 21; and the marriages are to the
births as 3 is to 4.
At Paris the baptisms of children of both sexes vary a little from the
ratio of 22 to 21. Since 1745, the epoch in which one has commenced to
distinguish the sexes upon the birth-registers, up to the end of 1784,
there have been baptized in this capital 393386 boys and 377555 girls.
The ratio of the two numbers is almost that of 25 to 24; it appears then
at Paris that a particular cause approximates an equality of baptisms of
the two sexes. If we apply to this matter the calculus of probabilities,
we find that it is a bet of 238 to 1 in favor of the existence of this
cause, which is sufficient to authorize the investigation. Upon
reflection it has appeared to me that the difference observed holds to
this, that the parents in the country and the provinces, finding some
advantage in keeping the boys at home, have sent to the Hospital for
Foundlings in Paris fewer of them relative to the number of girls
according to the ratio of births of the two sexes. This is proved by the
statement of the registers of this hospital. From the beginning of 1745
to the end of 1809 there were entered 163499 boys and 159405 girls. The
first of these numbers exceeds only by 1/38 the second, which it ought
to have surpassed at least by 1/24. This confirms the existence of the
assigned cause, namely, that the ratio of births of boys to those of
girls is at Paris that of 22 to 21, no attention having been paid to
foundlings.
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