Question

Sam is rolling a number cube with the numbers 1, 1, 2, 2, 3, and 3 printed on it.

What is the probability that, if he rolls the cube twice, the sum of the numbers will add to 4?​

Answer 1

0.3333

Explanation:

You first need to see how many ways he can roll a sum of 4. There are 12 ways. Treat each face as it's own value. There are 2 of each number on the die, so each face of the die is it's own event.

The 12 ways..

1-2. Rolls a 1 with the one of the 1-faces, then rolls a 3 with either of the 3-faces on the second roll. This counts for 2 different sums of 4.

1 (first 1 face) - 3 (first 3 face)

1 (first 1 face) - 3 (second 3 face)

3-4. He rolls a 1 but it's a different face than the other one than the one he rolled above. This gives us 2 more sums of 4

1 (other 1 face) - 3 (first 3 face)

1 (other 1 face) - 3 (second 3 face)

That's 4 total ways, the same logic will apply for the two 2 faces, and the two 3 faces. Each will have 4 more outcomes, giving us 8 more

There are 36 total outcomes (6*6 = 36), so

P(sum of 4) = 12/36 = 0.3333