462 H. S. JENNINGS AND K. S. LASHLEY 



3. To determine the probability x of any given number k 

 of pairs, when n individuals are drawn: 



^ m\k\n-2kll-n + kl ^ ^ 



4. Having the probability Xi for any given number of pairs 

 ^1, to find the probability X2 for the next higher number k^: 



^2 = 2:1 — — ~— (4) 



4k2-{l — n + k2) 



5. To determine how probable it is that there should occur a 

 deviation from the most probable number of pairs as great as 

 that observed: 



Determine by (3) and (4) the probabilities for all numbers of 

 pairs deviating less than the given deviation. The sum of these 

 probabilities is the total probability for deviations less than that 

 observed; the difference between their sum and 1 is the total 

 probability of a deviation as high as that observed or given. 

 Dividing the probability for deviations less than that observed, 

 by the probability for deviations as high as that observed gives 

 the odds against a deviation so high as that observed. 



6. Stirling's formula for finding nl: 



where 



(! = — F27rn 



e = 2.7182818 (or log. 0.4342944819) 

 jr = 3.1415927 (or log. 0.4971498726) 

 V27r = 2.506628 (or log. 0.3990899342) 



