Manchester Memoirs, Vol. II. (1907), No. 16. 



Result of 

 Throw. 



Frequency 











I 



3 



2 



?5 



3 



55 



4 



1 10 



5 



208 



6 



223 



7 



179 



8 



129 



9 



64 



10 



1 1 



1 1 



2 



12 



1 



Imagine that I am before you and that I have 12 dice 

 in a dice-box. I shake it and throw them. The result 

 happens to be 7 dice with 4-or-more-bearing faces upper- 

 most. I pick up all the dice, put them back into the 

 dice-box, shake it and throw them again ; the result 

 happens to be 5 such dice. What I want you to observe 

 is that in this pair of throws the two throws which 

 compose it are absolutely independent of one another ; 

 the result of the second is not affected by the result of 

 the first ; a knowledge of the result of the first does not 

 help us to predict the result of the second. 



Let us think of some way of making the two throws 

 in such a pair dependent, of making the result of the 

 second affected by the result of the first, and of bringing 

 it about that a knowledge of the result of the first shall 

 help us to predict the result of the second. 



I suggest to you that a good way of doing this is to 

 leave half the dice, which formed the first throw, lying on 



