Question

Laurissa rolls two number cubes, each with the numbers 1 through 6. Laurissa adds the numbers that appear on the roll Which two sums have an equal chance of occurring?​

Answer 1

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

$S_1 = \{1,2,3,4,5,6\}$

$S_2 = \{1,2,3,4,5,6\}$

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)$$(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)$

Next, get the sample space;$S = \{2,3,4,5,6,7, 3,4,5,6,7,8, 4,5,6,7,8,9, 5,6,7,8,9,10, 6,7,8,9,10,11, 7,8,9,10,11,12\}$

Reorder from lowest to highest$S = \{2,3,3,4,4,4,5,5,5,5,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,9,9,9,9,10,10,10,11,11,12 \}$

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;

The two sums that have equal probability have the same frequency;

Hence;

2 and  12 have the same chance of occurring

4 and  10 have the same chance of occurring

5 and  9 have the same chance of occurring

6 and  8 have the same chance of occurring