This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1814 edition. Excerpt: ...may be found; for it is only considering the probability of the contrary happening so many times in succession, and deducting from unity, as in the last case; thus, the probability of throwing either an ace or a 6 the first throw with 2 dice? The probability of throwing 1 of the 4 other faces each 4. 4 ...
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This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1814 edition. Excerpt: ...may be found; for it is only considering the probability of the contrary happening so many times in succession, and deducting from unity, as in the last case; thus, the probability of throwing either an ace or a 6 the first throw with 2 dice? The probability of throwing 1 of the 4 other faces each 4. 4 16, 20 time is----=--; therefore, the difference, or--, 6. 6 36 ' '36' shows that the odds are 20 to 16, or 5 to 4, in favour of either an ace or a 6 being thrown with 2 dice; and, the probability of throwing either 1, 2, or 3, with 3 dice, is found by considering the probability of someone of the other 3.3.3 27 3 faces comma; up each time, as------., and b '6.6.6 216' 189 the difference to unity, or j-g, being 189 to 27, or 7 to 1 in favour of either 1,2, or 3, being thrown with 3 dice; which are precisely the odds against winning 3 times in succession, where the chances on each event are equal, as J_. J_. J 1_ J2. 2. 2--"8" By the terms of the respective powers in the binomial table, the probabilities may also be found; it is only making one of the letters denote the face or faces required, and the other letter the faces not required. In the probability of an ace being thrown with 4 dice, a will represent the ace = 1, and b the other faces = 5. Now, in the 4th power (equal to the number of dice or throws), the probability of b 625 b or the 5 faces winning 4 times, is r =, and 'a+o 1296' the other terms in the power show the chances for a or the ace to win, either once only, or twice only, or three times only, or all 4 times, as the terms are denoted by the index; a, or4a36, or6a263, or4a63, which added together, are 671, and the probability of a or the ace being thrown once 671 or oftener in the 4 trials is, as before....
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Add this copy of The Doctrine of Chances, Or, the Theory of Gaming, Made to cart. $65.14, good condition, Sold by Bonita rated 4.0 out of 5 stars, ships from Newport Coast, CA, UNITED STATES, published 2011 by Nabu Press.
