THE THEORY OF PROBABILITY. 237 



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. 217). 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 could show, is highly improbable. Several 

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

 ance of theory and experience. The celebrated naturalist, 

 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 Professor 

 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. 



Quetelet also tested the theory in a rather more com- 

 plete manner, by placing 20 black and 20 white balls in an 

 urn and drawing a ball out time after time in an 

 indifferent manner, each ball being replaced, before a 

 new drawing was made. He found, as might be expected, 

 that the greater the number of drawings made the more 

 nearly were the white and black balls equal in number. 

 At the termination of the experiment he had registered 

 2066 white and 2030 black balls, the ratio being ro2\ 



i ' Letters on the Theory of Probabilities,' translated by Dowries, 1849, 

 PP- 36, 37- 



