Page:Mind (New Series) Volume 9.djvu/96

 82 HUGH MACCOLL the chance of A being true caused by the addition of the hypothesis B to our data e. Take Figs. 5, 6, 7 as illus- E E E F.c5 Fic.6. F.c.7 trations. In each of these figures a point P is taken at random in the circle E, and the statements A and B respec- tively assert that P will be one of the points in the circle A, that it will be one of the points in the circle B. First take Fig. 5. Here we have S A _ A _ A _ AB _ A __!_ J_ _! B ~ B e " B " t 4 13 52' In Fig. 6 we have X A A A 8 B = B~7 In Fig. 7 we have AB B 12 = 0. _ A _^. AB _ A = J L _ _3 = J^ E~Ee TT " 4 11 44' Similarly we get inFig.5, 8-+ in Fig. 6, 8 ? = ; A Thus we see that in the conditions of Fig. 5 the dependence is positive ; in Fig. 7 negative ; and in Fig. 6 zero. In the technical language of chances the statements A and B are said to be independent in the conditions of Fig. 6. This signification of the word independent does not quite coincide with its ordinary meaning. When in probability we speak of two statements A and B as independent, we do not necessarily assert that there is no connexion (causal or other) between the events or circumstances to which they refer, but only that the addition of either statement to our