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The Principles of Probability and Approximations in Arithmetic

Published online by Cambridge University Press:  03 November 2016

W. Hope-Jones
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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.

Type
Research Article
Information
The Mathematical Gazette , Volume 9 , Issue 130 , July 1917 , pp. 105 - 113
Copyright
Copyright © Mathematical Association 1917

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