## Read e-book online A History of the mathematical theory of probability from the PDF

By Todhunter, I. (Isaac)

ISBN-10: 1178318060

ISBN-13: 9781178318067

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**Read Online or Download A History of the mathematical theory of probability from the time of Pascal to that of Laplace PDF**

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**Additional info for A History of the mathematical theory of probability from the time of Pascal to that of Laplace **

**Example text**

In his eleventh proposition he investigates in how many throws a player may undertake to throw twelve with a pair of dice. In his twelfth proposition he investigates how many dice a player must have in order to undertake that in one throw tlVO sixes at least may appear. The thirteenth proposition consists of the following problem. A and B. They aie shewn to be as 13 is to 11. BUYGEN8. 34. The fourteenth proposition consists of the following problem. A and B play with two dice on the condition that A is to have the stake if he throws six before B throws seven, and that B is to have the stake if he throws seven before A throws six; A is to begin, and they are to throw alternately; compare the chances of A and B.

The dissertation is also inchtded in the collectioB of the philOSQphical writings of Leibnitz edited by Erdmann, Berlin, 18410. ~io 44. Leibnitz constructs a table at the beginning of bis dis- 32 LEIBNITZ. sertation similar to Prulcal's Arithmetical Triangk, and applies it to find the number of the combinations of an assigned set of things taken two, three, four, ... together. In the latter part of his dissertation Leibnitz shews how to obtain the number of permutations of a set of things taken all together; and he forms the product of the first 24 natural numbers.

Caramuel's method with the fourteenth problem of Huygens's treatise is as follows. Suppose the stake to be 36 j then A's chance 46 SAUVEUR. at his first throw is :6' and :6 x 36 = 5; thus taking 5 from 36 we may consider 31 as left for B. Now B's chance of success in a single throw is .!. t is 51, may be considered the value 36' 36 of his first throw. ') 5 to A and 51 to B, as the value of their first throws respectively; then the remaining 251 he proposes to divide equally between A and B. , and then to B for his second throw 3~ of the remainder; and so on.

### A History of the mathematical theory of probability from the time of Pascal to that of Laplace by Todhunter, I. (Isaac)

by Ronald

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