Final answer:
The probability that the sum of the numbers rolled on two dice will not be 4 is 11/12. This is found by subtracting the number of ways to get a sum of 4 from the total number of possible outcomes, which are 36 for two six-sided dice.
Step-by-step explanation:
The student asks about the probability that the sum of the numbers rolled on two dice will not be 4. To determine this, first, we need to identify all possible outcomes when two dice are rolled and then find out which of these result in a sum of 4. There are a total of 6 x 6 = 36 possible outcomes when rolling two dice. The pairs that sum to 4 are: (1,3), (2,2), and (3,1), making 3 ways to get a sum of 4.
To find the probability of not getting a sum of 4, we subtract the number of successful outcomes for getting a sum of 4 from the total number of outcomes. So, the probability P(not 4) = 1 - P(sum is 4). Since there are 3 ways to get a sum of 4, P(sum is 4) = 3/36 or 1/12. Therefore, P(not 4) = 1 - 1/12 = 11/12. Thus, the probability that the sum is not 4 is 11/12.