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Mathematics, 08.10.2019 04:30 linaaaaa7
Consider the game of independently throwing three fair six-sided dice. there are six combi- nations in which the three resulting numbers can sum up to 9, and also six combinations in which they can sum up to 10: 9 = 1 + 2 + 6 =1+3+5 = 1+4+4 = 2+ 3+ 4 = 2+2 +5 = 3+3+3 10 = 1+3+ 6 = 1+ 4+ 5 = 2+2+6 = 2+3+5 = 2 + 4 + 4 = 3+3+4 this seems to suggest that the chances of throwing 9 and 10 should be equal. yet, a certain gambler in florence in the early xvii century (most likely, the grand duke of tuscany cosimo ii de medici) noticed that in practice it is more likely to throw 10 than 9. show that the probability to get a total of 10 is, in fact, larger than the probability to get a total of 9. (this problem was solved for the duke by galileo galilei.)
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Consider the game of independently throwing three fair six-sided dice. there are six combi- nations...
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