Question

the table shows all the possible sums when rolling two number cubes numbered 1 – 6. what is the probability that rolling two cubes results in a sum of 8? table with rows 1–6 (first column) and columns 1–6 (first row), with sums: row 1 (1): 2,3,4,5,6,7; row 2 (2): 3,4,5,6,7,8; row 3 (3): 4,5,6,7,8,9; row 4 (4): 5,6,7,8,9,10; row 5 (5): 6,7,8,9,10,11; row 6 (6): 7,8,9,10,11,12 options: \\(\frac{5}{12}\\), \\(\frac{2}{3}\\), \\(\frac{5}{36}\\), \\(\frac{1}{3}\\)

Explanation:

Step1: Find total possible outcomes

When rolling two number cubes (each with 6 faces), the total number of possible outcomes is \(6\times6 = 36\) (since for each face of the first cube, there are 6 faces of the second cube).

Step2: Find number of favorable outcomes (sum = 8)

Looking at the table:

• When first cube is 2, second is 6 (2 + 6 = 8)
• When first cube is 3, second is 5 (3 + 5 = 8)
• When first cube is 4, second is 4 (4 + 4 = 8)
• When first cube is 5, second is 3 (5 + 3 = 8)
• When first cube is 6, second is 2 (6 + 2 = 8)

So there are 5 favorable outcomes.

Step3: Calculate probability

Probability is the number of favorable outcomes divided by total outcomes. So probability \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}=\frac{5}{36}\)

Answer:

\(\frac{5}{36}\)