510 THE ROYAL SOCIETY OF CANADA 



ness of ladies even with an umbrella and rain-coat to venture out, 

 save for a necessary purpose, in the face of impending rain, a con- 

 servative estimate of the ratio will be 2 /3 or 2 out of 3, i.e., out of every 

 three ladies who, in such a territory and period of time, return to the 

 house under the above circumstances, two do so for shelter and one 

 for some other purpose, e.g., to get an umbrella or rain-coat. The 

 popular expression for this ratio is two to one (2:1), but the fractional 

 expression 2/3 is scientifically superior. To determine numerically 

 the probability of an event, some value must be assigned to absolute 

 certainty, or that state of the case where all the chances without ex- 

 ception are favorable. This value is usually taken as unity or 1, 

 so that a probability short of absolute certainty is always represented 

 by a proper fraction having for numerator the number of favorable 

 chances and for denominator the total number of favorable and unfavor- 

 able chances; and impossibility, or that state of the case where all 

 the chances without exception are unfavorable, is represented by 

 zero or 0. 



(Evidence, Part 2) : "Presently she reappeared carrying an 

 umbrella, and continued on her way." 



This addition to the evidence disproves the 1st probable conclu- 

 sion that the lady, abandoning an errand abroad, returned to the 

 house for shelter; but the evidence as extended afïords ground for 

 another conclusion, namely that the lady noticed the clouds and 

 therefore returned for the umbrella. At bottom, however, this is 

 only a probable conclusion. The evidence, even as extended by part 

 2, contains nothing that shows necessarily whether the lady noticed 

 the clouds or why she re-entered the house. The degree of likelihood 

 in favor of the 2nd probable conclusion will be fixed approximately 

 by the number of ladies who, within a given large extent of territory 

 and within a given lengthy period of time, emerge from their homes 

 under circumstances similar to those described and return for an 

 umbrella because they notice the clouds, as against the total number of 

 ladies who, within the same territory and period of time and under the 

 same circumstances return to the house and reappear presently with 

 an umbrella, whether this was because they noticed the clouds or for 

 any other reason. On this point, as in the 1st probable conclusion, 

 it is impossible to secure definite statistics, but the 2nd conclusion is 

 manifestly much more probable that the 1st (2/3 or 2:1) and its de- 

 gree of likelihood may be conservatively estimated to be at least 20/21 

 or 20:1, i.e., out of every twenty-one ladies who in such a territory and 

 period of time re-enter their homes under the above circumstances 

 and reappear presently with an umbrella, twenty do so because they 

 noticed the clouds and one does so for other reasons. 



