In Galileos time people thought that when three dice were rolled, a sum of 9 and a

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In Galileo’s time people thought that when three dice were rolled, a sum of 9 and a sum of 10 had the 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+3 10: 1+3+6, 1+4+5, 2+4+4, 2+ 3+ 5, 2+4+4, 3+3+4

Compute the probabilities of these sums and show that 10 is a more likely total than 9.

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