Math  /  Data & Statistics

QuestionRefer to the table below. Of the 36 possible outcomes, determine the number for which the sum (for both dice) is 6 . \begin{tabular}{|c|c|c|c|c|c|c|} \hline & \multicolumn{6}{|c|}{ Die 2 } \\ \hline Die 1 & 1\mathbf{1} & 2\mathbf{2} & 3 & 4\mathbf{4} & 5\mathbf{5} & 6\mathbf{6} \\ \hline 1\mathbf{1} & (1,1)(1,1) & (1,2)(1,2) & (1,3)(1,3) & (1,4)(1,4) & (1,5)(1,5) & (1,6)(1,6) \\ \hline 2\mathbf{2} & (2,1)(2,1) & (2,2)(2,2) & (2,3)(2,3) & (2,4)(2,4) & (2,5)(2,5) & (2,6)(2,6) \\ \hline 3 & (3,1)(3,1) & (3,2)(3,2) & (3,3)(3,3) & (3,4)(3,4) & (3,5)(3,5) & (3,6)(3,6) \\ \hline 4 & (4,1)(4,1) & (4,2)(4,2) & (4,3)(4,3) & (4,4)(4,4) & (4,5)(4,5) & (4,6)(4,6) \\ \hline 5 & (5,1)(5,1) & (5,2)(5,2) & (5,3)(5,3) & (5,4)(5,4) & (5,5)(5,5) & (5,6)(5,6) \\ \hline 6 & (6,1)(6,1) & (6,2)(6,2) & (6,3)(6,3) & (6,4)(6,4) & (6,5)(6,5) & (6,6)(6,6) \\ \hline \end{tabular}
One can roll a sum of 6 in \square way(s)

Studdy Solution
Count the number of pairs identified in STEP_1.
(1, 6)(2, 4)(3, 3)(4, 2)(5, 1) \begin{aligned} &\text{(1, 6)}\\ &\text{(2, 4)}\\ &\text{(3, 3)}\\ &\text{(4, 2)}\\ &\text{(5, 1)} \end{aligned}
There are 5 such pairs.
The number of ways to roll a sum of 6 with two dice is 5\boxed{5}.

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