Question

two dice are rolled what is the probability of getting on numbers on both dice

Answer 1

6/36
=1/6
1/6 is the correct answer

Answer 2

So first, let’s figure out the number of possible outcomes. Each has 6 possible outcomes (1, 2, 3, 4, 5, 6), so the combination of these two becomes 6 * 6 = 36.

In case you want to see why this is:

(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)

where the first number in the parenthesis is the outcome of the first die and the second number is the outcome of the second die.

Now, of these 36 possible combinations, how many show the same number? Six of them:

(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)

So then the probability of two rolled dice having the same number becomes 6/36, which reduces to 1/6.