two fair dice are tossed and the result is recorded find the

two fair dice are tossed and the result is recorded. find the probability of the event that the sum of the numbers on the two dice is 4 or more. round to 3 decimal places

Solution

Event to generate 4 or more = (1,3), (1,4), (1,5), (1, 6), (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).
then number of possibilities = 33

and total number of outcomes for 2 dices = 36

then the probability of the event that the sum of the numbers on the two dice is 4 or more = 33/36 = 11/12