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  3. 3.50 passedix is a game of chance played with thre

3.50 Passedix is a game of chance played with three fair dice. Players bet whether the sum...

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Basic Math

3.50

Passedix is a game of chance played with three fair dice.Players bet whether the sum of the faces shown on the dice will beabove or below ten. During the late sixteenth century, theastronomer and mathematician Galileo Galilei was asked by the GrandDuke of Tuscany to explain why “the chance of throwing a 9 withthree fair dice was less than that of throwing a 10.” (Interstat,Jan. 2004) The grand duke believed that the chance should be thesame because “there are an equal number of partitions of thenumbers 9 and 10.” Find the flaw in the Grand Duke’s reasoning andanswer the question posed to Galileo. Hint: What the Grand Duke wassaying is: There are six ways to get a 9: 1+2+6; 1+3+5; 1+4+4;2+2+5; 2+3+4; 3+3+3. There are also six ways to get a 10: 1+3+6;1+4+5; 2+2+6; 2+3+5; 2+4+4; 3+3+4. [10 pts] 3.56 Two fair dice aretossed, and the following events are defined: A: {Sum of thenumbers showing is odd} B: {Sum of the numbers showing is 9, 11, or12} Are events A and B independent? Why? [10 pts]

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