PEOFESSOR PEARSON'S CONTRIBUTIONS TO OSTEOLOGY. 459 



_ We shall now proceed to describe briefly the nature of the 

 ' error curve.' 



The Probability Curve. — Consider any compound event ^ whicli 

 is the result of the concurrence of n similar simple events. J Let 

 the chances of the occurrence or failure of each primary event 

 be P/Q, so that P + Q = l, 



Let (P + Q)'^ be expanded by the binomial theorem, thus 



(P+Qf = P« + «P«-iQ+!^::l!^)pn---'Q-^+ 



wPQ"-i + Q» 



Then, from the principles of probability (see any Algebra) 

 it can be readily shown that the first term ia this expression 

 is the probability that all will happen; the second that n — l 

 will happen and 1 fail; the third that n — 2 will happen 

 and 2 fail ; and so on to the last term, Q", which is the 

 probability that all will fail. 



Take for example the case of the throwing of coins. Let 

 8 coins be tossed concurrently. 



ThenP = Q = ^ 



and ?i = 8 

 and the binomial series becomes 



K2^2) -256^256^256^256 + 256 

 56 28 8 1 

 "^256 + 256 + 256 + 256 

 Hence the probability 



1 



256 



8 



that all are heads is 

 that 7 are heads and 1 tails is 

 that 6 are heads and 2 tails is 



256 

 28 



256 

 and so on. 



^ " A compound event is one produced by the concurrence of several primary 

 or simple events, each being independent of the other. For instance, throwing 

 three aces with three dice in one trial is a compound event produced by the con" 

 currence of tiiree simple events."— Merriman, Method pf Least Squares. 



