Probable in a Correlated System of Variables. 1 69 



improbable, if the chance of all the faces is alike and equal 

 to 1/6 th. 



Illustration III. 

 In the case of runs of colour in the throws of the roulette- 

 ball at Monte Carlo, I have shown* that the odds are at 

 least 1000 millions to one against such a fortnight of runs as 

 occurred in July 1892 being a random result of a true roulette. 

 1 now give ^ 2 for the data printed in the paper referred 

 to, i.e.: 



4274 Sets at Roulette. 



• 



1 



246: 

 2137 



2 



945 



1068 



3 



333 

 534 



4 



220 



267 



5 



135 

 134 



6 



81 

 67 



7 



43 

 33 



8 



30 

 17 



9 



12 



8 



10 



7 

 4 



11 



5 

 o 



12 



1 

 1 



Over 

 12 



. Actual ... 

 Theory . . . 





 



From this we find ^ = 172 43, and the improbability of a 

 series as bad as or worse than this is about 14*5/10 3 ° ! From 

 this it will be more than ever evident how little chance had to 

 do with the results of the Monte Carlo roulette in July 1892. 



(7) Frequency of General Population not knoivn a priori. 



Illustration IV. t 

 In my memoir on skew-variation (Phil. Trans, vol. clxxxvi. 

 p. 401) I have fitted the statistics for the frequency of petals 

 in 222 buttercups with the skew-curve 



y = -211225^- 322 (7-3253-a?) 3 - 142 . 



The possible range is from 5 to 11 petals, and the fre- 

 quencies are : — 





No. of Petals... 



5 



6 



7 



8 9 



10 



2 



0-8 



11 





Observation ... 

 Theory 



133 

 136-9 



55 



48-5 



23 

 22-6 



7 2 

 96 3-4 





 02 







These lead to ^ — 4*885,528 ; whence we find for the pro- 

 bability of a system of deviations as much or more removed 



* ' The Chances of Death,' vol. i. : The Scientific Aspect of Monte 

 Carlo Roulette, p. 54. 



t Illustrations IV. and V. were taken quite at random from my 

 available data. Other fits with skew-curves may give much worse 

 results, others much better, for anything I can as yet say to the contrary, 



