Answer:
2 and 12;
4 and 10;
5 and 9
6 and 8
Step-by-step explanation:
Given
Roll of two number cubes
Required
Determine the sums which have equal chance
Represent the sample space of both number cubes with S1 and S2
![S_1 = \{1,2,3,4,5,6\}](https://tex.z-dn.net/?f=S_1%20%3D%20%5C%7B1%2C2%2C3%2C4%2C5%2C6%5C%7D)
![S_2 = \{1,2,3,4,5,6\}](https://tex.z-dn.net/?f=S_2%20%3D%20%5C%7B1%2C2%2C3%2C4%2C5%2C6%5C%7D)
Next, get the outcome of roll two number cubes
Outcome = ![(1,1)(1,2)(1,3)(1,4)(1,5)(1,6)\ (2,1)(2,2)(2,3)(2,4)(2,5)(2,6)\ (3,1)(3,2)(3,3)(3,4)(3,5)(3,6)](https://tex.z-dn.net/?f=%281%2C1%29%281%2C2%29%281%2C3%29%281%2C4%29%281%2C5%29%281%2C6%29%5C%20%282%2C1%29%282%2C2%29%282%2C3%29%282%2C4%29%282%2C5%29%282%2C6%29%5C%20%283%2C1%29%283%2C2%29%283%2C3%29%283%2C4%29%283%2C5%29%283%2C6%29)
![(4,1)(4,2)(4,3)(4,4)(4,5)(4,6)\ (5,1)(5,2)(5,3)(5,4)(5,5)(5,6)\ (6,1)(6,2)(6,3)(6,4)(6,5)(6,6)](https://tex.z-dn.net/?f=%284%2C1%29%284%2C2%29%284%2C3%29%284%2C4%29%284%2C5%29%284%2C6%29%5C%20%285%2C1%29%285%2C2%29%285%2C3%29%285%2C4%29%285%2C5%29%285%2C6%29%5C%20%286%2C1%29%286%2C2%29%286%2C3%29%286%2C4%29%286%2C5%29%286%2C6%29)
Next, get the sample space;![S = \{2,3,4,5,6,7, 3,4,5,6,7,8, 4,5,6,7,8,9, 5,6,7,8,9,10, 6,7,8,9,10,11, 7,8,9,10,11,12\}](https://tex.z-dn.net/?f=S%20%3D%20%5C%7B2%2C3%2C4%2C5%2C6%2C7%2C%20%20%20%20%203%2C4%2C5%2C6%2C7%2C8%2C%20%20%20%204%2C5%2C6%2C7%2C8%2C9%2C%20%20%20%20%205%2C6%2C7%2C8%2C9%2C10%2C%20%20%20%20%206%2C7%2C8%2C9%2C10%2C11%2C%20%20%20%20%20%20%207%2C8%2C9%2C10%2C11%2C12%5C%7D)
Reorder from lowest to highest![S = \{2,3,3,4,4,4,5,5,5,5,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,9,9,9,9,10,10,10,11,11,12 \}](https://tex.z-dn.net/?f=S%20%3D%20%5C%7B2%2C3%2C3%2C4%2C4%2C4%2C5%2C5%2C5%2C5%2C6%2C6%2C6%2C6%2C6%2C7%2C7%2C7%2C7%2C7%2C7%2C8%2C8%2C8%2C8%2C8%2C9%2C9%2C9%2C9%2C10%2C10%2C10%2C11%2C11%2C12%20%5C%7D)
Next, form a frequency table
Sum -- Frequency
2 ---- -- 1
3 ---- -- 2
4 ---- -- 3
5 ---- -- 4
6 ---- -- 5
7 ---- -- 6
8 ----- -- 5
9 - ------ 4
10 --- -- 3
11 --- ---- 2
12 ------ 1
From the above table, we can now determine the two sums that have equal probability;
<em>The two sums that have equal probability have the same frequency;</em>
Hence;
<em>2 and 12 have the same chance of occurring</em>
<em>4 and 10 have the same chance of occurring</em>
<em>5 and 9 have the same chance of occurring</em>
<em>6 and 8 have the same chance of occurring</em>