ESSAY ON PROBABILITIES. 



RULE. (TABLE L) 

 Divide twice the product of 

 a and b by their sum, and ex- 

 tract the square root of the 

 quotient, by which divide k. 

 Then the last quotient being 

 't, the H of the table is 

 probability required. 



the 



RULE. (TABLE II.) 



Having found the square 

 root, and divided k by it, as 

 opposite, from seven times the 

 quotient, take the hundredth 

 part of the quotient, and take 



three tenths of the remainder. 

 Make the result t, and K in 

 the table is the probability re- 

 quired. 



Suppose that in a thousand trials, A has happened 

 exactly 6*00 times, and B 400 times ; what is the pre- 

 sumption that the odds for A against B lie between 570 

 to 430 and 630 to 370 ? 



600,6 = 400, = 30. 



2 x 600 x 400 = 480,000 



480,000 

 1000 



= 480 



V480 =21-91 

 SO 



H = 94713 



1-369 

 7 



9-583 

 014 



9-569 

 3 



28-707 t = 2- 871 

 K= -94719 



Answer. About 95 to 5, or 19 to 1 in favour of the 

 odds being between the limits specified. N 



In the preceding problem, A and B have happened a 

 and b times; whence the most likely of all individual cases 

 is, that the odds for A against B are a to b; or, in other 

 words, the result which has the strongest presumption 

 in its favour is, that 



Probability of A was 



a + b. 



Probability of B was r 



a + b' 



Now we have found, in the preceding problem, the 

 presumption that 



Probability of A lies between and J 



a + b a+b 



