Page:Philosophical Transactions - Volume 053.djvu/479

 Suppoe, further, that he has heard 40 blanks drawn and 4 prizes; what will the before-mentioned chances be?

The anwer here is .1525, for the former of thee chances; and .527, for the latter. There will, therefore, now be an odds of only 5$1⁄2$ to 1 againt 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 les than 9 to 1.

Once more. Suppoe he has heard 100 blanks drawn and 10 prizes.

The anwer here may till be found by the irt rule; and the chance for a proportion of blanks to prizes les than 9 to 1 will be .44109, and for a proportion greater than 11 to 1 .3082. It would therefore be likely that there were not fewer than 9 or more than 11 blanks to a prize. But at the ame time it will remain unlikely that the true proportion hould lie between 9 to 1 and 11 to 1, the chance for this being .2506 &c. There will therefore be till an odds of near 3 to 1 againt this.

From thee calculations it appears that, in the circumtances I have uppoed, the chance for being right in gueing the proportion of blanks to prizes to be nearly the ame with that of the number of blanks Vol. LIII