C H A 



>. II' an event may happen in <t ways, and fail in I ways, any of these 



being equally probable, the chance of its happening is ^ j and the 



a -{- b 



chance of its failing is 



a-f b' 



EA\ 1 . The probability of throwing an ace with a single die in one trial 

 is ; the probability of not throwing an ace is ^ ; and the probability 



of throwing an ace or a deuce is ~. 



Ex. 2. If n balls a, b, c, d, &c. be thrown promiscuously into a bag, and 

 if two balls be drawn out, the probability that these will be a and b is 

 2 



n(n-\.)' 



3. If two events be independent of each other, and the probability that 

 one will happen be , and the probability that the other will happen 



; the probability that they will both happen is . 



<7o>-. 1. The probability that both do not happen is mn ~ l t 



Cor. 2. The probability that they will both fail is ~ . ? 



mn 



Cor. 3. The probability that one will happen, and the other fail, is 

 m 4. n 2 

 m n x 

 Cor. 4. If there be any number of independent events, and the proba- 



bilities of their happening be , , c. respectively, the probabi- 



lity that they will all happen is - &c. When m n r &c. the 

 yn n r 



probability is - , ? being the number of events. 

 m v 



F,J\ \. The probability of throwing an ace and then a deuce with one 



Ex. 2. If 6 white and 5 black balls be thrown promiscuously into a bag, 

 the probability that a person will draw out first a white, and then a black 

 57 



