Bauhaus-Universität Weimar

The New Psychology
Scripture, Edward Wheeler
accurately defined as depending on the number of 
throws. That is done in the following way :— 
Suppose that we establish a scale of certainty ex¬ 
tending from for positive results down to for negative results. If a black face is to 
be expected with a certainty of we know 
absolutely that it will appear ; such would be the case 
if all the faces were black. If it is to be expected with 
a certainty of, then no black face would appear; 
such would be the case if all the faces were white. Let 
us see what certainty we are to attach to the fraction £ 
when we say that at any given throw with our original 
die the odds are i to 5 for the black. The solution has 
been found by Bernoulli. If 11 throws are to be made 
with our die, we can expect with a certainty of 
P=4> (r) + -0= 
V2 7T 1lpq 
that the actual result differs from the ideal probability 
p=i by an amount which lies between 
± k=± yJÏE 
^ 11 
The expression $ (y) is the well-known probability- 
function. A table of its values will be found as 
Appendix I. The quantity e is the basis of the natural 
system of logarithms, or=2.71828. 
For example, supposing we are to make 3000 throws 
with the die, with how much certainty may we expect 
that the black face will appear not more than 505 times 
or less than 495 times ; or, in other words, that it will 
not differ from the ideal J by more than + 3o50 (j- = ? 
Here we have 11=3000, p=i, q=%, and y S/2J?=


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