68 ESSAY ON PROBABILITIES. 



of the letters A, B, and C : that is, to all appearance, 

 we have this strange result ; the chances of drawing 

 one of the three, A, B or C, are greater than those of 

 drawing one of the set, A or B, or C or D, &c. &c. up 

 to Z. This paradox will afford me a good opportunity 

 of again inculcating the maxim, that the probability of 

 an event is the presumption drawn from certain obvious 

 principles, as to what the state of our minds ought 

 to be with regard to belief in the happening of that 

 event, as influenced by our knowledge of previous 

 events. Consequently, if John know that A, B, and 

 C have been drawn 49, 37, and 14 times, and nothing 

 more, he has reasonable ground, with his knowledge, 

 for assenting to the proposition that the 101st trial 

 shall give either A, B, or C, as to a proposition 

 which has ^-g-J of probability, or 103 to 1 in its 

 favour. But if Thomas only know that 100 draw- 

 ings have all given letters, then he, with his know- 

 ledge, has no ground of inference with respect to A, B, 

 and C, in particular, but may reasonably assent to the 

 proposition, " the 101st drawing will also give a letter," 

 as having a probability of j-g 4, or 101 to 1 in its 

 favour. But the paradox in question requires that 

 John should make believe he knows no more than 

 Thomas, and then be surprised that a discordance 

 should arise from his using that knowledge in recon- 

 sidering a result, which he has suppressed in the me- 

 thod of attaining it. 



It very rarely happens that we meet with a case in 

 which we can so distinctly specify the antecedent cir- 

 cumstances which influence our assent or dissent, as to 

 enable us to apply direct calculation to the determin- 

 ation of the rational probability of an event to come. 

 And in most of the practicable cases, the largeness of 

 the numbers employed would check our progress, if it 

 were not for the approximative methods of the higher 

 mathematics, and the tables at the end of this work. I 

 now proceed to the method of using those tables. 



