MATHEMATICAL SECTION. 89 
26TH MEETING. Marca 16, 1887. 
The Chairman presided. 
Present, sixteen members. 
Mr. CuristI& read a paper on 
A PROBLEM IN PROBABILITIES. 
In this paper he reviewed the conditions of the question in prob- 
abilities discussed at the previous meeting. He considered it a 
question susceptible of a detinite answer, dependent only on a logi- 
cal and mandatory application of the elementary principles of prob- 
ability. In his analysis he derived expressions for the possible 
combinations of the several events and deduced therefrom a func- 
tion representing the probability of the probability of the compound 
event (rottenness and worminess), the variable in this function being 
the probability sought. The value of the variable making the func- 
tion a maximum was taken as the required probability, the result 
being 545. 
If nm = total number of apples, 7 = number rotten, w= number 
wormy, «= number both rotten and wormy, then 
@@+1) w+) (ae L) Ga Dd) , ; 
a? Te eo —lor”’>2z>2", 
and the chance of a particular apple being both rotten and wormy 
/ 
is =, When # and” are integral the chance is either of or 4 , that 
gt 2” 
a When n, 7, w are all infinite, the case of continuous 
is 
: . Tw 
number, this chance is ar 
Mr. Stone took the ground that the problem is susceptible of but 
one interpretation, and gave a geometric solution leading to zs for 
the probability of the compound event. He also gave some in- 
stances of allied questions in dependent probabilities. : 
An animated discussion, extending over the remaining time of - 
the meeting, then followed. Of those who participated in the dis- . 
cussion, Messrs. CHRISTIE, Curtis, Doouirrye, Exuiorr, Hr11, 
KUMMELL, STONE and Zrwer considered the problem determinate, 
while Messrs. BAKER, Harkness, and Woopwarp considered it 
indeterminate. 
