C H A 



ball, is . And the probability of drawing a white ball, and then two 



black balls is 1. 



Ex. 3. The probability of throwing an ace with a single die in two trials 

 . II 



15 38- 



4. If the probability of an event's happening in one trial be -r, the 



probability of its happening 1 1 times exactly in n trials is 

 _ # _i_ i t n-i 



(a + b) n 

 Cor. 1. The probability of the event's failing exactly^ times in n trials 



n-1 jt-2 n-* + l -< 

 n . - . - r- 2 * 



(a + b} n 



Cor. 2. The probability of the event's happening at least t times in n 

 trials, is 



n n- 1 



(a + V n 



b. In astronomical or other observations, let a, b, c, d, &c. be the dif- 

 ferences between the mean of the observations, and the observations 

 themselves ; n the number of observations ; a- = 3. 14159 &c. ; then the 

 mean error, or the greatest probable error is 



La Pla 



6. Let n be the number of times an event has happened, where n is 

 very large, then the chance that the same event will occur again is 



? . Thus supposing 5000 years the greatest antiquity to which his- 

 n + * 



tory goes back ; then the probability that the sun will rise to-morrow is 

 1826211 to 1. (La Place.) 



58 



