Question

If you roll two fair six-sided dice, what is the probability that the sum is 555 or lower?

Answer 1

It would be 5/18

Explanation:

An easy way is to count outcomes. Of the 36 equally probable outcomes, 10 are less than or equal to 5, so the probability is 10/36 = 5/18.

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Answer 2

Rolling a two six-sided dice means we would have (6x6) = 36 combinations.

(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)

It says to find the combinations whose sum is 5 or lesser. Those favorable combinations would be :-

(1,1) (1,2) (1,3) (1,4)

(2,1) (2,2) (2,3)

(3,1) (3,2)

(4,1)

So we have favorable 10 combinations.

Probability is the ratio of Favorable combinations to Total combinations.

Probability = 10/36 = 5/18