Question

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

Answer 1

Answer:

I will use the notation:

Cube1 + Cube2 = sum.

Ok, each number cube has 6 options, so the total number of possible combinations is equal to the product of the number of options for each event we have two events (two number cubes).

Then:

C = 6*6 = 36

we have 36 possible combinations.

Now, let's look at the sums that have the same number of combinations (which would mean that have the same number of combinations).

For example, the lower result possible is two ones:

1 + 1 = 2

(only one outcome adds up to 2)

And the maximum result possible is two sixes:

6 + 6 = 12

(only one outcome adds up to 12)

Then 2 and 12 have the same probability, 1/36.

Now we can keep loking at 2 + 1 and 12 - 1.

2 + 1 = 3

The outcomes that add up to 3 are:

1 + 2 = 3

2 + 1 = 3

(two outcomes out of 36)

12 - 1 = 11

The outcomes that add up to 11 are:

6 + 5 = 11

5 + 6 = 11

(Two outcomes out of 36)

Then 3 and 11 have the same probability, 2/36.

And we can notice the pattern here.

4 and 10 will have the same probability 3/36

5 and 9 will have the same probability 4/36

6 and 8 will have the same probability 5/36

7 is the only option that does not have a pair, the probability is 6/36.