SOLUTION: What is the probability that the sum is less than or equal to 9 in three rolls of a die ?

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Question 1177819: What is the probability that the sum is less than or equal to 9
in three rolls of a die ?
Answer by ewatrrr(24785) (Show Source):
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Hi three rolls of a die: 6^3 = 216 ways they can be rolled. • 3 = 1 + 1 + 1 , 1 way • 4 = 1 + 1 + 2 , 3 ways * 3!/2! • 5 = 1 + 1 + 3 = 2 + 2 + 1, 6 ways 3!/2! + 3!/2! • 6 = 1 + 1 + 4 = 1 + 2 + 3 = 2 + 2 + 2 10ways 3!/2! + 3! + 1 • 7 = 1 + 1 + 5 = 2 + 2 + 3 = 3 + 3 + 1 = 1 + 2 + 4 , 15 ways etc • 8 = 1 + 1 + 6 = 2 + 3 + 3 = 4 + 3 + 1 = 1 + 2 + 5 = 2 + 2 + 4, 21 ways • 9 = 6 + 2 + 1 = 4 + 3 + 2 = 3 + 3 + 3 = 2 + 2 + 5 = 1 + 3 + 5 = 1 + 4 + 4, 25 ways P(sum ≤ 9) = 1+3 +6+10+15+21+25 = 81/6^3 = 81/216 = 3/8 Wish You the Best in your Studies.