Math  /  Discrete

QuestionAssume two six-sided dice are rolled each with the numbers 1,2,3,4,51,2,3,4,5, and 6 . The first one is red and the second one is green. Use a systematic listing to determine the number of ways to roll a total less than 7 on the two dice.

Studdy Solution
Count the number of outcomes where the sum is less than 7: - From red die outcome 1 1 : (1,1),(1,2),(1,3),(1,4),(1,5) (1, 1), (1, 2), (1, 3), (1, 4), (1, 5) (5 outcomes) - From red die outcome 2 2 : (2,1),(2,2),(2,3),(2,4) (2, 1), (2, 2), (2, 3), (2, 4) (4 outcomes) - From red die outcome 3 3 : (3,1),(3,2),(3,3) (3, 1), (3, 2), (3, 3) (3 outcomes) - From red die outcome 4 4 : (4,1),(4,2) (4, 1), (4, 2) (2 outcomes) - From red die outcome 5 5 : (5,1) (5, 1) (1 outcome)
Total number of outcomes: 5+4+3+2+1=15 5 + 4 + 3 + 2 + 1 = 15 .
The number of ways to roll a total less than 7 is:
15 \boxed{15}

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