THE THEORY OF PROBABILITY. 231 



Three combinations give 2 tails. Probability f . 



One combination gives 3 tails. Probability ^. 

 We could apply the same considerations to the ima- 

 ginary causes of the difference of stature, the combina- 

 tions of which were shown in p. 213. There are alto- 

 gether 128 ways in which seven causes can be combined 

 together. Now, twenty-one of these combinations give 

 an addition of two inches, so that the probability of a 

 person under the circumstances being five feet two inches 

 is ~-. The probability of five feet three inches is ~ 8 ; 

 of five feet one inch is ^~ ; of five feet ^Is* an( ^ so OD - 

 Thus the eighth line of the Arithmetical Triangle gives all 

 the probabilities arising out of the combinations of seven 

 causes or things. 



Rules for the Calculation of Probabilities. 



I will now explain as simply as possible the rules 

 for calculating probabilities. The principal rule is as 

 follows : 



Calculate the number of events which may happen 

 independently of each other, and which are as far as 

 is known equally probable. Make this number the de- 

 nominator of a fraction, and take for the numerator the 

 number of such events as imply or constitute the hap- 

 pening of the event, whose probability is required. 



Thus, if the letters of the word Roma be thrown down 

 casually in a row, what is the probability that they will 

 form a significant Latin word ? The possible arrange- 

 ments of four letters are 4x3x2x1, or 24 in number 

 (p. 201), and if ah 1 the arrangements be examined, seven 

 of these will be found to have meaning, namely Roma, 

 rarno, oram, mora, maro, armo, and amor, Hence the 

 probability of a significant result is / 



f Wallis ' Of Combinations/ p. 117. 



