110 Probability 



together, whether the penny turns up head has absolutely no 

 bearing on whether the dime is head or tail. They are two 

 independent events. If they are tossed together, the chance 

 that the penny will be head is % and the chance that the dime 

 will be head is % ; the chance that both will be head is % X /4 or 

 %. Whenever there are two independent events, the chance 

 that both will occur together is the chance that one will occur 

 multiplied by the chance that the other will occur. For example, 

 if the chance that team A beats team B in football is %, and the 

 chance that team C beats team D in basketball is %, the chance 

 that both A and C will win is % X -/^ oi" "K2- Similarly, the 

 chance that both the penny and the dime will be tail is ^. In 

 the same way, the chance that the penny will be head and the 

 dime tail at the same time is % X Vz or ^, and the chance of a 

 simultaneous tail on the penny and head on the dime is %. If 

 the denominations of the coins are disregarded, and the only point 

 considered is the chance that either one will be a head while 

 the other is a tail, the chance is ^ + % or %. In sex, which we 

 discussed earlier, the chance that a certain child will be a boy 

 is % and the chance is also % that the same child will be a girl. 

 If there are two children the chance that both will be boys is 

 %, the chance that one will be a boy and the other a girl is %, 

 and the chance that both will be girls is ^4- 



If three coins are tossed at a time, the chance of three heads 

 is /^ X % X % or %, and the same is true of three tails. The 

 chance of two heads and a tail is % and the chance of one head 

 and two tails is the same. The chance that three children will be 

 boys is similarly %, and the chance that all will be girls is also 

 Yg. In a family of three, the chance of getting two boys and a 

 girl is % and the chance of one boy and two girls is also %. The 

 algebraic-minded student will begin to see that this fits in with 

 the binomial theorem, which is generally expressed by (a + b)^. 

 In problems dealing with probability, this is usually written 

 iv + 9)", where p is the chance that a certain event will happen, 

 q the chance that it will not happen, and n is the number of 

 individuals concerned in the event. In sex, p could represent 

 the chance that an individual would be a boy, and would be %, 

 and q would represent the chance that the child would not be a 

 boy (and, therefore, the chance of its being a girl) and would 



