8 Ellery W. Davis 



Continuity required that which was above and beyond all law;i 

 required chance. \ 



So in our study of the universe, though we find a continual 

 approximation to law, still there is always something that baf- 

 fles us, something that no law seems to reach. Chance or 

 something that we fail to distinguish from chance plays its 

 part. 



But what is chance? Can we give a definition? 



Consider the familiar example of coin tossing. It is an 

 even chance, we say, whether heads or tails shall turn up. 

 Toss up ten coins. The chance is that about five heads and 

 five tails will be shown. Notice the "about." Were the coins 

 tossed a thousand times it would be remarkable if always five 

 heads and five tails showed. We should suspect a cause for 

 svich regularity. Is causelessness, then, a mark of chance? 

 Suppose irregularity, might not it also have a cause? 



Consider again the single coin. Why do we say it is an 

 even chance whether heads or tails turn up? Is this anything 

 more than saying we don't know any reason why one rather 

 than the other should turn up, a mere taking of the agnostic 

 position? The turning up of heads is simply one of two pos- 

 sibilities, and we refuse to commit ourselves to a belief in the 

 happening of this rather than of the other. 



Take now the case of ten coins. Here there are eleven pos- 

 sibilities: all heads; nine heads, one tail; eight heads, two 

 tails; and so on. Would our agnosticism require us to say 

 that these possibilities were equally probable? To some it 

 may. To the mathematician d'Alembert, all events, since 

 they must either happen or not happen, seemed to have the 

 probability one-half. But we need not be quite so ignorant. 

 Plainly into our judgment of the chances should enter not 

 only the possible number of happenings, but also the num- 

 ber of ways in which each is possible. Now all heads is pos- 

 sible in only one way; but nine heads, one tail is possible in 



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