hr ON PROBABILITY. 
Yata, 
th- 2 22 2° 
¢? = 14 iw~—+ &e. 
1.2 
. 2 
‘L122 4+ 82,...+ Pisthe coefficient of = in e222, ,.. 8%) 
é (¢® EE 1) er — 1 
TEL TIT 
sy Pa Pa? 
gr ¢ + 5 e — + &e. 
ox 
1—=+4 == &ec 
jerrg=—it 
If we effect the division of Z,, 4 “the three first terms will be 
] — + =~ — &c. 
2 at 
Fr 
found to be 1 + 2 x: * and all beyond involve higher powers of x than 
2 : ” 
the square, and therefore need not be considered. Multiplying ¢ + = 
4% 2% @ a2 : a? 284-3241 
the (hin “J 5 by 1 3 + Ve get for the coefficient of Th Hoa 
therefore 
re iE dd y 
1 E% LEE PAPE) 
Ze 6 6 
0 and the probability in question is 
2a Jit 1) (2i + Dip @itt 2 
i.i4 1 6 = 3 > 
When 7 is very great, this fraction approximates to 22 ; if, therefore, 
the ratio of the white balls may be any ratio between 0 and unity, that is, if 
we have no data to determine that some of these values are more probable 
fi than others, i z = 1, and this probability is £. 
ry 48. Let the ratio of the white balls to the whole number of balls, be any of 
of the following, A 2,2 A 2,3 A ......¢ A x, and consequently the ratio 
2 of the black balls to the whole number of balls, 
3h 1- Az1—2A71=8Az......1—iA® 
and let m white balls have been drawn, and 7 black, in any given order. 
The probability of the event observed on the hypothesis that 2 A 2 is the 
method of ratio of the white balls to the whole number of balls is 
use it fur- (m—+n).(m4+n=1)........1 : or " 3 
te sme Fy nT Ti Uanalaia 
and the probability of this hypothesis is 
Gaz)"(l —i Az) 
Am(L-Aaay+@Az"(~—2A a) &e 
The probability of drawing m’ white balls, and #/ black balls, in 7m’ -- n’/ 
future trials upon this hypothesis, is 
0k