Final answer:
To find the probability of getting a total of 3 with two dice, we consider the two possible outcomes adding up to 3, leading to the probability of 1/18. For the probability of getting at most a total of 11, we find that there are 35 outcomes adding up to 11 or less out of 36 possible outcomes, yielding a probability of 35/36.
Step-by-step explanation:
The question asks us to calculate probabilities involving rolling dice, which is a common problem in probability theory within mathematics. To calculate the probability of getting a total of 3 when two fair six-sided dice are rolled, we must look at all possible outcomes that can sum up to 3.
This can occur in two ways: (1,2) and (2,1). Since there are 6 possible outcomes for each die, the total number of possible outcomes when two dice are rolled is 6 x 6 = 36. Thus, the probability of rolling a total of 3 is 2/36, which simplifies to 1/18.
Part b of the question requires finding the probability of rolling at most a total of 11. This comprises all the possible sums from 2 to 11, which are all possible sums except 12. The only way to get a sum of 12 is by getting a double six (6,6), which is 1 outcome out of 36. Therefore, the probability of getting at most a total of 11 is 35/36 as there are 35 outcomes that sum to 11 or less.