(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)′.

  (Logic Operations and Equivalence MC)Use the statements and truth table to determine which statements are equivalent. p: It is a university. q: It offers a degree in aviation management. p q ∼p ∼q p → q ∼p → ∼q q → p ∼q → ∼p T T F F T T T T T F F T F T T F F T T F T F F T F F T T T T T T

Hematopoiesis occurs in the _______ bone marrow.

(Exponential Models MC)The level of fame of an artist is assigned from 1 to 10, with 10 signifying the most famous artist. Data are collected about selling prices for painting and the level of fame of the artists. The model ŷ = 948.25(2.998)x is calculated, where x represents the artist’s fame score and ŷ represents the predicted selling price of the painting. Use the model to predict the selling price of a painting whose artist’s fame is a level 4.