ON DIRECT PROBABILITIES. 



there is about an even chance of one success in 100 

 throws. 



A table of the number of trials (odds being n. to 1) 

 in which there are various odds of succeeding once : 



The method of using this table is as follows : Sup- 

 pose the odds to be 20 to 1 against success in a single 

 trial : required in how many throws it is 100 to 1 there 

 shall be one success (or more). Look in the table 

 opposite to " 100 to I/' and we see 4-62 ; multiply 20 

 by 462 and divide ly 100 (which is always to be done), 

 this gives 92 fa, or 92 is about the number of throws 

 required. 



I now proceed to the method of compounding the 

 probabilities of single events, so as to find those of com- 

 pound events : that is, the way of methodising the re- 

 sults of actual inspection. 



Let there be two events, one of which may happen in 7 

 ways, and may not happen in 5; and the other of which 

 may happen in 4 ways, and may not happen in 9 ' 

 whence the probabilities of the two events (A and B) 

 are T V and -*-%. Now, the compound event may hap- 

 pen in 12 X 13 different ways, for any case of the first 

 (12 in all) may come up with any case of the second 

 (13 in all). By similar reason, the compound case in 

 which both A and B happen may come up in 7 X 4 

 different ways ; hence the probability of A and B both 

 happening, is 



-jlil which is the product of 1 and _ 

 RULE. When events are perfectly independent, so 



