This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1738 Excerpt: ... obliges himself in a certain number os throws n with a pair of common Dice not only to throw the Chances v and vi, hut v before vi, with this restriSiion, that if he happens to throw v before vi, he does not indeed lose his wager; but is to proceed as if nothing had been done, still deducing so many throws as have ...
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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1738 Excerpt: ... obliges himself in a certain number os throws n with a pair of common Dice not only to throw the Chances v and vi, hut v before vi, with this restriSiion, that if he happens to throw v before vi, he does not indeed lose his wager; but is to proceed as if nothing had been done, still deducing so many throws as have been vain from the number of throws which he had at first given him; to find the Probability of his winning. Solution. Let the number of Chances which there are for throwing v be called a, the number of Chances for throwing vi, b; the number of all the Chances upon two Dice J, and the number of throws that A takes =qB n. This being supposed, i." If A throws v the first throw, of which the Probability is--he has nothing more to do than to throw vi in n--i times, (c)f which the Probability is I----------, and therefore the Probability of throwing v the first time, and throwing afterwards " 7=--'" vi m n--i times is-r x i--. / /--2. If A misses v the first time, and throws it the second, of which the Probability is " x-, then he is afterwards to throw----v. tf--2 vi in n--2 times, of which the Probability being i--J, it follows that the Probability of miffing v the first time, throwing h the second, and afterwards throwing vi, will be /-x 4 XI--4 3. If y4 misses v the two first times, and throws it the third, then he is afterwards to throw vi in n--3 times, the Probability of all which is Ielju-l X-xi-/=r"i and so on jjow // s f=n--i all this added together constitutes two geometric Progressions, the number of whose Terms in each is n---1. Wherefore the Sum of the whole will be /'-'_7=r"-' __ mr--ab v jr=rg--' _jrr7 if a and b are equal, then the second part will be reduced to----i xax.s--aYx. Now...
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Add this copy of The Doctrine Of Chances to cart. $19.72, new condition, Sold by Ingram Customer Returns Center rated 5.0 out of 5 stars, ships from NV, USA, published 2022 by Legare Street Press.
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Add this copy of The Doctrine of Chances to cart. $75.87, new condition, Sold by Bonita rated 4.0 out of 5 stars, ships from Newport Coast, CA, UNITED STATES, published 2022 by Legare Street Press.
