A standard pair of six-sided dice is rolled. What is the probability of rolling a sum greater than or equal to 4

Answer 1

In this case, it may be easier to find the complement of the question. That is:

You are asked to find P(Sum > 4), this is equal to 1 - P(Sum < 4).

Consider the following (Dice 1, Dice 2):

(1, 1)

(1, 2)

(2, 1)

P(Sum < 4) = 3/36 = 1/12

These are the only combinations for the dice to sum to a value less than 4. Therefore, of the 36 possible combinations, 3 are removed, leaving you with 33/36 possible combinations.

P(Sum > 4) = 1 - P(Sum <4) = 1 - (1/12) = 11/12 (which is exact)

You could also say P(Sum > 4) ~ 0.917 or 91.7%