CHOICE AND CHANCE. 39 
and is probably safe, although delayed. In the event itself there is no uncertainty. 
The vessel has either sunk or not. Nevertheless the probabilities will vary with 
different persons, and in the same person from day to day, as information is re- 
ceived in regard to storms at sea, signs of wreck picked up, the trustworthiness 
of her officers, etc.” Finally after all have united in believing the vessel lost, she 
sails into port. While the general opinion is still the same, a few on land know 
that she is safe. Those on the vessel have never been in doubt about it. 
In order to understand more clearly the application and importance of the 
Theory of Probability, let us take a single example : 
Let us suppose that we have an urn, containing a large number of equal 
balls, and for simplicity, let us suppose that half are white, the others black. 
Draw from the urn any number of balls at once, say six, (of course without 
choosing) and repeat this drawing a large number of times (say 1,000) replacing 
the balls and shaking them up each time. Set down each time the.number of 
white balls drawn. There are seven possible chances, viz: 
; 6 white and o black. 
5 66 ce I 66 
4 6c a) 66 
3 (a 66 3 66 
6c 66 6c 
e 2 4 
I 66 ce 5 6c 
fo} 6é 66 6G (3 
We all know something in regard to the probability in each of these cases. 
We should meet least frequently with the two extreme cases—all white and all 
black—and in the long run we should meet with one as many times as with the 
other, since there is nothing in color or lack of color which could affect the 
chances in drawing. 
The following table gives the distribution of the number of draws out of 100 
for each of the possible cases. The greater the number of draws, the more nearly 
these values would be obtained: 
Chances. No. of Times. 
White. Black. 2 
6 
5 66 ome 
4 (a 
2 
2 
I 
fe) 
fe) 
I 
2 Gua 
66 3 6c 36 
3 4 66 24 
Gs 5 3 
6 
C6 6 
100 
That is, we should draw 6 white balls twice out of each hundred draws, etc. 
These numbers can be quite accurately determined by 1,000 draws, if the urn 
contain several hundred balls * 
i *These numbers represent the successive terms of the expanded binomial (% plus %)6 where the sum 
of the terms is taken as 100, and where the exponent represents the number of balls drawn at once. 
