An Introduction to a Biology 



result of each throw will be common to the two throws of a 

 pair. 



But you will say, " How will you know which six dice 

 to leave on the table ? You will not be able to help leaving 

 the ones showing 4-or-more down and picking up the others, 

 except by making it a rule not to do so. And that would 

 introduce too much complication. It seems to me that it 

 will be very difficult to make the decision as to which dice 

 shall be picked up and which not a matter of chance and 

 not of choice." This objection is quite reasonable, but the 

 difficulty is not insurmountable. All that is necessary is to 

 make six of the dice different from the other six. This is 

 easily effected by leaving them for a few hours in red ink. 

 It does not matter whether we make it our rule to leave 

 the red or the white dice down on the table when we gather 

 up the six dice to make the second throw. Let us decide on 

 the red. 



We can now start to make a pair of connected throws, in 



which the decision as to which dice pass over undisturbed 



from the first to the second throw is a matter of chance and 



not of choice. I put all the dice — the 6 red and the 6 white 



— into the dice box, shake it about, and throw the dice on 



to the table. The result happens to be 6.^ Now I gather 



up the white dice, put them into the dice box, and throw 



them. In describing the results of the second throw I count 



the red as well as the white, although only the latter have 



been thrown a second time. So that half of the results which 



determine the total result of the first throw are exactly the 



same as half of those which determine the total result of 



the second. The two throws are connected together. For 



instance, let us consider the maximum possible difference 



between the two connected throws and compare it with the 



maximum possible difference between two independent 



^ The number describing the result of a throw means the number of 

 dice exhibiting faces with four-or-more pips on them uppermost in that 

 throw. 



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