(Applying Two-Way Frequency Tables MC)A social media company tracked the professions of 290 users who watched different types of videos and displayed the data in a table. Beauty Tips Contests Interviews Reveals Artist 31 5 11 16 Student 29 15 19 14 Engineer 12 17 21 17 Nurse 8 23 29 23 Is being an artist independent of watching contests for these social media users? Justify your conclusion.

(Conditional Probability LC)The probability of selecting a red marble is 0.41. The probability of selecting a red marble, given that the marble is glass, is 0.59. Interpret the outcome of the conditional probability.

(Applying Two-Way Frequency Tables LC)P(A) = 0.27, P(B) = 0.40, and P(A∩B) = 0.670. Are events A and B independent? Justify the answer mathematically.

(Interpreting Independence HC)The table summarizes the daily caffeine habits and majors of students at one university. Coffee Energy Drink No Caffeine STEM Major 0.32 0.13 0.02 Not STEM Major 0.17 0.27 0.09 Part A: Determine P(no caffeine | STEM major) and describe the event in everyday language. Show all work. (5 points)Part B: Are the events consuming no caffeine and a STEM major approximately independent? Use probabilities to justify the answer. (5 points)

(Addition and Multiplication Rules for Probability LC)P(A) = 0.53, P(B) = 0.21, and P(B | A) = 0.53. Are the events independent? Justify mathematically.

(Addition and Multiplication Rules for Probability LC)P(A) = 0.33, P(B) = 0.47, and P(A ∪ B) = 0.80. Are events A and B mutually exclusive? Justify mathematically.

(Combinations and Permutations LC)Calculate the number of combinations, given n = 6 and r = 3.

(Combinations and Permutations MC)A spelling bee has 22 contestants. In how many ways can they finish in first, second, and third place?

(Addition and Multiplication Rules for Probability LC)P(A) = 0.61, P(B) = 0.15, and P(A ∪ B) = 0.76. Are events A and B mutually exclusive? Justify mathematically.

(Set Operations and Relations MC)Given U = {g, h, i, j, k, l, m, n, o, p}, A = {g, h, m, o, p}, and B = {h, j, k, m, n, p}. If A′ ∩ B′ = {i, l}, determine (A ∪ B)′.