1. The problem states: An urn contains 12 white, 5 yellow, and 13 black marbles. A marble is chosen at random and it is known it is not black. Step 1: Find the sample space given the marble is not black. Total marbles not black = 12 (white) + 5 (yellow) = 17 Sample space = \{white, yellow\} Step 2: Find the probability the marble is yellow given it is not black. Probability(yellow) = number of yellow marbles / total non-black marbles = $\frac{5}{17}$ 2. The problem: Two fair dice are rolled. a. Probability space: Each die has 6 faces; total outcomes = $6 \times 6 = 36$ b. Probability sum is 7: The pairs that sum to 7: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) = 6 outcomes Probability = $\frac{6}{36} = \frac{1}{6}$ c. Probability both dice show 2: Only one outcome: (2,2) Probability = $\frac{1}{36}$ 3. The problem: In a city, coffee drinkers = 65%, tea drinkers = 50%, both = 25%. Step 1: Calculate probability drinking at least one (coffee or tea): Using inclusion-exclusion: $$ P(C \cup T) = P(C) + P(T) - P(C \cap T) = 0.65 + 0.5 - 0.25 = 0.9 $$ Step 2: Probability drinking neither coffee nor tea: $$ 1 - P(C \cup T) = 1 - 0.9 = 0.1 $$ Final answers: 1. Sample space is the set of non-black marbles: white and yellow (17 total). Probability yellow given non-black = $\frac{5}{17}$. 2a. Total outcomes rolling two dice = 36. 2b. Probability sum is 7 = $\frac{1}{6}$. 2c. Probability both dice show 2 = $\frac{1}{36}$. 3a. Probability drinks at least one (coffee or tea) = 0.9. 3b. Probability drinks neither = 0.1.