122 THE QUANTITATIVE METHOD IN BIOLOGY 



First and Second Series : looo Tosses 



According to the above figures, the simple event 

 a (head) has been observed 1483 times 

 b (tail) „ „ „ 1517 „ 



The observed ratio is heads -.tails = o-gy8:i, the calculated 

 ratio being 1:1. In § 93 (3000 tosses) the observed ratio was 

 heads : tails = o-gg6 : i. (See § 103.) 



§ 96 .—FIFTH EXAMPLE : POSITIONS OF EQUI- 

 LIBRIUM OF A SYSTEM OF n COINS.— Whatever may be 

 the number of coins, complete information about all the possible 

 events is obtained by means of the expression (a + &)", in which 



(i) a and b represent the simple events (a = head and b = tail) ; 



(2) a = b = l (frequency of the simple events) ; 



(3) w = number of coins (number of simple events which are 



combined into compound events). 

 Let us suppose that six coins, I., II., III., IV., V. and VI., are 

 tossed. The order of succession being taken into account, 

 sixty-four compound events are equally possible (stable) — ^viz. 



aaaaaa aaaaah aaaabh aaabbb bbbbaa bbbhba bbbbbb 



