What are the odds of rolling two number cubes and getting a sum of seven?

Solution:

If two dice are rolled together, the sample space of outcomes 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)

⇒ Total number of outcomes(sample space) = 36

Getting the sum 7 (favourable outcomes) = (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1).

⇒ Probability of Getting a sum 7 = Number of favourable outcomes / Total number of outcomes.

⇒ P = 6 / 36

⇒ P = 1 / 6

What are the odds of rolling two number cubes and getting a sum of seven?

Summary:

The odds of rolling two number cubes and getting a sum of seven is 1/6.