THE THEORY OF PROBABILITY. 231 



Three combinations give 2 tails. Probability f. 



One combination gives 3 tails. Probability -J-. 

 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 Y~* The probability of five feet three inches is ~^ ; 

 of five feet one inch is ~ ; of five feet r ~-g, and so on. 

 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 all the arrangements be examined, seven 

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

 ramo, or am, mom, maro, armo, and amor. Hence the 

 probability of a significant result is -/^. f 



f Wallis ' Of Combinations,' p. 117. 



