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#6. In Galileos time people thought that when three dice were rolled, a sum of 9 and sum of 10 had same probability since each could be obtained in 6 ways: 9: 1+2+6, 1+3+5, 1+4+4, 2+2+5, 2+3+4, 3+3+310: 1+3+6, 1+4+5, 2+4+4, 2+3+5, 2+2+6,3+3+4. Compute the probabilities of these sums and show that 10 is a more likely total than 9

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Answer 6)

The probability of the sum of the numbers shows that 9 is obtained below: Let S denote the sample space when three 6-sided dice is rolled. Let E denote the event that the sum of the number shows that 9 The total outcomes of a pair of six-sided dice is, 61,0 62(0.6.3,.(6.6,1,.(0.4,5,.(0.% That is, N (S) 216 That is, N(E) 25. The required probability is216 0.1157The probability of the sum of the numbers shows that 10 is obtained below: Let F denote the event that the sum of the number shows that 10 It is, The required probability is, P (F) N) NTS 27 0.125The probability of the sum of the numbers shows that 10 is 0.125. The probability of the sum of the numbers shows that 9 is 0

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