ON INVERSE PROBABILITIES. 6j 



winning, it is now 14 out of 23, and 1 chance out of 

 23 remains for the next game being drawn. 



When a number of different events have happened, 

 A, B, C, &c., write down each number increased by 1, 

 and the results will express the several relative proba- 

 bilities, on the supposition that no events can happen 

 except those which have happened. But if new events 

 may happen, write down 1 for the relative probability 

 of such an occurrence at the next trial. Thus, if out 

 of a box, and in 100 drawings, there have appeared 49 

 white balls, 37 red, and 14 black ; then if it be known 

 that nothing but white, red, or black can appear, con- 

 sider the chances of these to be as 50, 38, and 15 ; that 

 is, -j 5 ^ is the chance of drawing a white ball at the 

 101st trial. But if another sort of ball may appear., 

 then the chances of the four cases being as 50, 38, 15, 

 and 1, it follows that -ffy is the chance of a white ball 

 at the 101st trial. 



In judging of future events by those which have 

 passed, we must be extremely cautious always to pre- 

 serve the same method of considering the event pro- 

 posed. If, for instance, in ] 00 trials, A has appeared 

 49 times, B 37 times, and C 14 times, we know that 

 there is one chance out of 104 that the 101st drawing 

 shall give neither A, B, nor C, but something else. 

 What the new character may possibly be is left un- 

 known ; it may be another letter, or it may be a num- 

 ber, a picture, or a blank. Are we to understand that 

 all these are equally probable ? Common sense tells us 

 the contrary ; experience makes us feel it much more 

 likely that the letter D should appear at the 101st trial,, 

 than any stated number or picture. But we have 

 now changed the question, and, dropping the distinction 

 between A, B, and C, have considered them merely as 

 letters. Having drawn a letter 100 times running, we 

 are to infer (page 64.) that it is 101 to 1 in favour 

 of our drawing a letter at the 101st trial; or that |g-J 

 is the chance of this. But it is already 103 to 1 that 

 the next drawing shall be, not merely a letter, but one 

 F 2 



