C 413 ] 
Suppofe, further, that he has heard 40 blanks 
drawn and 4 prizes j what will the before-mention- 
ed chances be ? 
The anfwer here is .1525, for the former of thefe 
chances j and .527, for the latter. There will, there- 
fore, now be an odds of only 54. to 1 againft the 
proportion of blanks to prizes lying between 9 to 1 
and 11 to 1 ; and but little more than an equal chance 
that it is lefs than 9 to 1. 
Once more. Suppofe he has heard 100 blanks 
drawn and 10 prizes. 
The anfwer here may ftill be found by the firffc 
rule ; and the chance for a proportion of blanks to 
prizes lefs than 9 to 1 will be .44109, and for a pro- 
portion greater than n to 1 .3082. It would there- 
fore be likely that there were not fewer than 9 or 
more than 1 1 blanks to a prize. But at the fame time 
it will remain unlikely * that the true proportion 
fhould lie between 9 to 1 and 11 to 1, the chance 
for this being .2506 &c. There will therefore be 
ftill an odds of near 3 to 1 againft this. 
From thefe calculations it appears that, in the cir- 
cumftances I have fuppofed, the chance for being 
right in guefting the proportion of blanks to prizes to 
be nearly the fame with that of the number of blanks 
* I fuppofe no attentive perfon will find any difficulty in this. 
It is only faying that, fuppofing the interval between nothing 
and certainty divided into a hundred equal chances, there will be 
44 of them for a lefs proportion of blanks to prizes than 9 to r, 
31 for a greater than 1 1 to 1, and 25 for fome proportion be- 
tween 9 to 1 and 11 to ij in which it is obvious that, though 
one of thefe fuppofitions muft be true, yet, having each of them 
more chances againft them than for them, they are all feparately 
unlikely. 
Vol. LIJI. Hhh drawn 
