Question

(8 points) In the early 1600s, Galileo was asked to explain the fact that, although the number of triples of integers from 1 to 6 with sum 9 is the same as the number of such triples with sum 10, when three dice are rolled, a 9 seemed to come up less often than a 10 - supposedly in the experience of gamblers. Explain why the gamblers' report of their experience is correct. Support your answer with calculations of appropriate probabilities. To count, list systematically

Answer 1

Sol nteger coming threc be on despectively there 6X6XG Can be number of Ways X, ,X, omd X 216 (a) number ce, 2)-3! y- 6 (s,21223y total Ways (G,1,3,-6 ys (6, 3 Ways (5, 2,3) 3 ways -3 ways Can of of way um Hence total humber 6+3t3t3 t = 18 ways occur since fnthree tess than ay that 9 comes can We afce ame