Question

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

Answer 1

Answer:

Let's analyze the possible sums of both dices, i will use the notation:

Dice1 + Dice 2 = sum.

also remember that we have 2 dices, with 6 options each.

So the total number of combinations is 6*6 = 36

we have 36 possible outcomes.

I will start at the extremes, the minimum that we can sum is 2, and the maximum is 12, then:

We can have 2 if:

1 + 1 = 2

only one permutation.

and 12 if:

6 + 6 = 12

Again, only one permutation.

so 2 and 12 have the same chance (1 out of 36)

now, to have 3 we can have:

2 + 1 = 3

or

1 + 2 = 3.

and to have 11

5 + 6 = 11

6 + 5 = 11

Again, 3 and 11 have the same probability (2 out of 36 options)

And now we can see a pattern.

4 and 10 will have the same chance.

5 and 9 will have the same chance

6 and 8 will have the same chance

7 is the only number that has an unique chance (and it has the largest one)