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