bility required, and therefore the
probability required is in all 1/6 + 5/36 = 11/36.

To this case is analogous a question commonly proposed about throwing
with two dice either six or seven in two throws, which will be easily
solved, provided it be known that seven has 6 chances to come up, and
six 5 chances, and that the whole number of chances in two dice is 36;
for the number of chances for throwing six or seven 11, it follows that
the probability of throwing either chance the first time is 11/36, but
if both are missed the first time, still either may be thrown the second
time; but the probability of missing both the first time is 25/36,
and the probability of throwing either of them on the second is 11/36;
therefore the probability of missing both of them the first time, and
throwing either of them the second time, is 25/36 X 11/36 = 275/1296,
and therefore the probability required is 11/36 + 275/1296 = 671/1296,
and the probability of the contrary is 625/1296.

Among the many mistakes that are committed about chances, one of the
most common and least suspected was that which related to lotteries.
Thus, supposing a lottery wherein the proportion of the blanks to
the prizes was as five to one, it was very natural to conclude that,
therefore, five tickets were requisite for the chance of a prize; and
yet it is demonstrable that four tickets were more than sufficient
for that purpose. In like manner, supposing a lottery in which the
proportion of the blanks to the prize is as thirty-nine to one (as was
the lottery of 1710), it may be proved that in twenty-eight tickets a
prize is as likely to be taken as not, which, though it may contradict
the common notions, is nevertheless grounded upon infallible
demonstrations.

When the Play of the Royal Oak was in use, some persons who lost
considerably by it, had their losses chiefly occasioned by an argument
of which they could not perceive the fallacy. The odds against any
particular point of the ball were one and thirty to one, which entitled
the adventurers, in case they were winners, to have thirty-two stakes
returned, including their own; instead of which, as they had but
twenty-eight, it was very plain that, on the single account of the
disadvantage of the play, they lost one-eighth part of all the money
played for. But the master of the ball maintained that they had no
reason to complain, since he would undertake that any particular point
of the ball should come up