•ilO TREMBLE Y. 



probability qua Viteaux, la 2:)ossibilite des naissances des filles est 

 superieure h celle des naissances des gardens; in the Theorie... 

 des F7vh. he says, la superiorite de la facilite des naissances des 

 filles, est done indiquee par ces observations, avec une probabilite 

 egale k '67. These phrases seem much better adapted to the idea 

 to be expressed than Trembley's, Probabilitas numerum puellarum 

 superaturum esse numerum puerorum erit = •67141. 



770. Trembley now takes the following problem. From a 

 basf containing; white balls and black balls in a larg^e number but 

 in an unknown ratio j^ white balls and q black have been drawn ; 

 required the chance that if 2a more drawings are made the white 

 balls shall not exceed the black. This problem leads to a series 

 of which the sum cannot be found exactly. Trembley gives some 

 investigations respecting the series which seem of no use, and of 

 which he himself makes no application ; these are on his pages 

 103 — 105. On his page 106 he gives a rough approximate value 

 of the sum. He says, Similem seriem refert Gel. la Place. This 

 refers to the Hist de V Acad.... Paris for 1778, page 280. But the 

 word similem must not be taken too strictly, for Laplace's approxi- 

 mate result is not the same as Trembley's. 



Laplace applies his result to estimate the probability that more 

 boys than girls will be born in a given year. This is not repeated 

 in the Theorie... des Proh., but is in fact included in what is there 

 given, pages 397 — 401, which first appeared in the Hist, de 

 r Acad.... Paris for 1783, page 458. 



771. Trembley now takes another of Laplace's problems, 

 namely that discussed by Laplace in the Memoires . . . par divers 

 So.vans, Vol. vi. page 633. 



Two players, whose respective skills are unknown, play on the 

 condition that he who first gains 7i games over his adversary shall 

 take the whole stake ; at a certain stage when A wants f games 

 and B wants h games they agree to leave off playing : required 

 to know how the stake should be divided. Suppose it were given 

 that the skill of ^ is a? and that of jB is 1 — x. Then we know 

 by Art. 172 that B ought to have the fraction <j) (x) of the stake, 

 where 



