Final answer:
The probability that the sum of two rolled six-sided dice is strictly more than 3 is 11/12 since there are 33 successful outcomes out of a total of 36 possible outcomes.
Step-by-step explanation:
You are rolling two fair and independent six-sided dice. The probability that the sum of the two dice is strictly more than 3 can be calculated by considering the total number of possible outcomes and the number of successful outcomes that fulfill the condition.
Each die has 6 faces, so when rolling two dice, the total number of possible outcomes is 6 x 6, which equals 36. The only sums that are not more than 3 are 2 (1+1) and 3 (1+2, 2+1). Since there are 3 outcomes with a sum of 3 or less, there are 36 - 3 = 33 successful outcomes where the sum is strictly more than 3.
The probability is the number of successful outcomes divided by the total number of possible outcomes: P(sum > 3) = 33 / 36. This simplifies to 11/12.