Question

If you roll two number cubes ,what is the probability of their sum being 9 or higher?

Answer 1

5/18

Explanation:

When two cubes are rolled there are 36 possibilities

Each dice has 6 equally like outcomes so possibilities are

(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)

Now we look at the pair that has sum equal to 9

(3,6) (4,5) (5,4) (6,3) that has sum of 9

Probability of sum is 9 =
`(4)/(36)`

we look at the pairs that has sum greater than 9

(4,6) (5,5)(5,6) (6,4)(6,5)(6,6)

Probability of sum greater than 9 =
`(6)/(36)`

Probability of sum 9 or higher = P(sum 9) + P(greater than 9)

=
`(4)/(36)+(6)/(36)= (10)/(36)=(5)/(18)`