x.] THE THEORY OF PROBABILITY. 207 



possible experience. It might happen that a person 

 should always throw a coin head uppermost, and appear 

 incapable of getting tail by chance. The theory would 

 not be falsified, because it contemplates the possibility of 

 the most extreme runs of luck. Our actual experience 

 might be counter to all that is probable ; the whole 

 course of events might seem to be in complete contra- 

 diction to what we should expect, and yet a casual con- 

 junction of events might be the real explanation. It is 

 just possible that some regular coincidences, which we 

 attribute to fixed laws of nature, are due to the accidental 

 conjunction of phenomena in the cases to which our 

 attention is directed. All that we can learn from finite 

 experience is capable, according to the theory of probabili- 

 ties, of misleading us, and it is only infinite experience 

 that could assure us of any inductive truths. 



At the same time, the probability that any extreme 

 runs of luck will occur is so excessively slight, that it 

 would be absurd seriously to expect their occurrence. It 

 is almost impossible, for instance, that any whist player 

 should have played in any two games where the distri- 

 bution of the cards was exactly the same, by pure accident 

 (p. 191). Such a thing as a person always losing at 

 a game of pure chance, is wholly unknown. Coincidences 

 of this kind are not impossible, as I have said, but they 

 are so unlikely that the lifetime of any person, or indeed 

 the whole duration of history, does not give any appreciable 

 probability of their being encountered. Whenever we 

 make any extensive series of trials of chance results, as in 

 throwing a die or coin, the probability is great that the 

 results will agree nearly with the predictions yielded by 

 theory. Precise agreement must not be expected, for that, 

 as the theory shows, is highly improbable. Several 

 attempts have been made to test, in this way, the accord- 

 ance of theory and experience. Buffon caused the first 

 trial to be made by a young child who threw a coin many 

 times in succession, and he obtained 1992 tails to 2048 

 heads. A pupil of De Morgan repeated the trial for his 

 own satisfaction, and obtained 2044 tails to 2048 heads. In 

 both cases the coincidence with theory is as close as could 

 be expected, and the details may be found in De Morgan's 

 " Formal Logic," p. 185. 



