Probability 109 



number of individuals, the greater the margin of safety when 

 deahng with probabiHties. One polled calf tells nothing. 



"What is the probability that in a family of four all will be 

 boys? Is the chance that there will be three boys and one girl 

 greater or less than the chance that all four will be boys? Both 

 are possible, so the question becomes one of probability. The 

 ratio of men to women is actually about 106 : 100, but for prac- 

 tical purposes it can be assumed that the chances are even, i.e., 

 1 : 1, or more popularly "fifty-fifty." Since, as we are assuming, 

 it is equally probable that one child will be either male or female, 

 the problem is identical with the problem of whether a toss of a 

 coin will result in a head or a tail. That is a problem more 

 familiar to most people, so let us consider it first. If a penny is 

 tossed into the air, the chances are even that it will land head 

 or tail. AVith one toss, the chance of a head is % and of a tail, 

 ^2- The word "chance" does not imply that it is not a question 

 of cause and effect. The effect after tossing the coin is a head 

 or a tail, but the causes which determine that effect are numerous. 



One cause is the way the coin is held in the hand. Another 

 cause is the exact motion of the fingers and arm as the penny is 

 being tossed. The height of the toss is still another factor for 

 if the height had been a trifle less, the other side, other things 

 being equal, would have turned up. The amount of spin to the 

 coin, air currents as the coin is ascending and descending, the 

 precise way the coin hits the ground, whether it strikes a smooth 

 place or a slight bump in the ground, whether it rolls or lands 

 dead, how much it rolls — all these are causes that work together 

 to produce the effect. However, these causes are too difficult to 

 measure and too numerous to analyze. Furthermore, all are not 

 working in the same direction. Some of these causes tend to 

 make the penny turn up a head; other causes tend to make it a 

 tail. By chance is meant that the effect is produced by a very 

 large number of causes, some of which act in one direction and 

 some in the other direction, some may be greater in effect and 

 some lesser, and all or most defy analysis. In other words, when 

 an effect is not produced by one or a few readily observed causes, 

 it is said to be due to chance. 



When a penny is tossed, the chance of a head is %. The 

 same is true of a dime. If a penny and a dime are tossed 



