Final answer:
To construct a sample space for rolling two dice one after the other, pair each possible outcome from the first die roll with each possible outcome from the second die roll. The probabilities for different sums are: a) 6 - 5/36, b) 36 - 0, c) 11 - 1/18, and d) 12 - 1/36.
Step-by-step explanation:
To construct a sample space for rolling two dice one after the other, we need to list all possible outcomes. Let's call the first die roll 'X' and the second die roll 'Y'. Each die has 6 sides, so the sample space is created by pairing each possible outcome from X with each possible outcome from Y. For example, if X is 1 and Y is 1, the outcome is (1, 1). The sample space would be:
{(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), ..., (6, 5), (6, 6)}
To determine the probability that the sum of the dots on the dice totals:
a) 6: Count the number of outcomes where the sum is 6 (5 outcomes: (1, 5), (2, 4), (3, 3), (4, 2), (5, 1)) and divide it by the total number of outcomes (36). The probability is 5/36.
b) 36: There are no outcomes where the sum is 36, so the probability is 0.
c) 11: Count the number of outcomes where the sum is 11 (2 outcomes: (5, 6), (6, 5)) and divide it by the total number of outcomes (36). The probability is 2/36 = 1/18.
d) 12: Count the number of outcomes where the sum is 12 (1 outcome: (6, 6)) and divide it by the total number of outcomes (36). The probability is 1/36.