Final answer:
The probability of rolling a sum of 7 or 11 with two fair six-sided dice is 2/9, as there are 8 favorable outcomes of a total of 36 possible outcomes when rolling the dice.
Step-by-step explanation:
The question involves calculating the probability of the sum of dots being either 7 or 11 when two fair six-sided dice are rolled. In this probability experiment, we first identify all the possible combinations that would result in the sum of dots being 7 or 11.
To obtain a sum of 7, we have the following combinations: (1,6), (2,5), (3,4), (4,3), (5,2), and (6,1), which totals 6 outcomes. To obtain a sum of 11, there are the combinations: (5,6) and (6,5), which totals 2 outcomes. This gives us a total of 8 favorable outcomes for 7 or 11.
Since there are a total of 36 outcomes when rolling two six-sided dice (6 outcomes for one die multiplied by 6 outcomes of the other die), we can find the probability by dividing the favorable outcomes (8) by the total outcomes (36): P(7 or 11) = 8/36 = 2/9.
The correct answer is therefore: A. 2/9.