/)/:"f7./ r/o.v or R.-ixinnt .v./.w/7.c,v 91 



present the teleplume prohlem. Of course, only a bird's-eye view 

 ol the the<)r\- will lie ^iven liere. Se\eral lacuniT; will he encountered; 

 the tilling in of an\' one of tlu-ni would call for a volunu' of not ver\' 

 small dimensions. 



Inirodic HON I'o Tiir: TiU'Dkn oi "A 1'(>sii;ki(>ki " 



i'KOHAHIUTY 



The prohlem U> he dealt with helongs to the class of problems which 

 ^ave rise to that branch of the Theory of Probability which is known 

 as "A Posteriori Probability" or "Probahilit\' of Causes." It is 

 frequently referred to as the Theory of Samplinj;. 



To bring out certain of the ideas involved it will be helpful to 

 consider what may appear as a very extreme example from the traffic 

 man's point of view, hut which is nevertheless typical of the type of 

 prohlem in which a consiileration of a posteriori probabilit>- enters. 

 \Vc are told that at a student gathering a particular young man won 

 7 out of 15 times. Our informant refuses to di\ulge what is going 

 on at the gathering. What prnh.iliiliiio should we assign to the 

 following hypotheses .■" 



1. He threw heads 7 times out of lo throws with a coin. 

 "2. He threw 7 aces out of 15 throws with a G face die. 



3. He won on points 7 rt)unds in a fifteen round bout. 



4. The aggregate of all other hypotheses. 



A little careful consideration will make it clear tliat witii reference 

 to each hypothesis (or aggregate of hypotheses) two essential ques- 

 tions must be answered before we can determine the a posteriori 

 probability. Consider the six face die hypothesis; we must know: 



1st — What is the relative frequency or probability with which 

 gambling with a 6 face die is indulged in at student gatherings? 



2nd — Given a six face die, what is the probability of throwing an 

 ace 7 times in 15 throws? 



Quoting Mr. .-\rne Fisher' we may restate these two (piestions as 

 follows: 



1st —What is the a priori existence probability in favor of the ti 



face die hypothesis? 

 2nd — What is the productive probahilil\' for the observed event 



given by the hypothesis of a (i face die? 

 ' Arne Fisher — The Mathematical Theory of Probabilities — 2nd Edition — .Art. 41. 



