The Principles of Probability and Approximations in Arithmetic

Extract

If n quantities, which are known to the nearest whole number, are added together, find the probability that their sum so obtained is correct to the nearest whole number.

Let the probability that the error is between x and x + dx be p dx.

If n = 2, and x>0,

p dx=Probability that first error is between x – 1/2 and 1/2,

and that second error is within a given dx of its possible range

from – 1/2 to 1/2,

= (1– x)dx ; ∴ p = 1–x.

If x<0, p = 1+x.