26 THE ROYAL SOCIETY OF CANADA 



Problem 3. Two points are taken at random on a given line 

 of length a; the chance that the distance between them shall exceed 



a given length c is I j 









y 



&^2. 



Probability required 



'a /~y— c 



dx dy 

 : J o 

 a / y 



dx dy 

 ' o 



(") 



i.e., if a = 100, we get, according as c = 25, 50 or 75, probability; 



56i 25 6i 



, or . 



100 100 100 



