(Addition and Multiplication Rules for Probability LC)P(A) = 0.44, P(B) = 0.44, and P(A ∪ B) = 0.78. Are events A and B mutually exclusive? Justify 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(energy drink | STEM major) and describe the event in everyday language. Show all work. (5 points)Part B: Are the events consuming energy drinks and a STEM major approximately independent? Use probabilities to justify the answer. (5 points)

(Logic Operations and Equivalence MC)Use the statements and truth table to determine which statements are equivalent.p: It is a burger.q: It has ketchup on it. p q ~p ~q p → q ~q → ~p q → p T T F F T T T T F F T F F T F T T F T T F F F T T T T T

(Logic Operations and Equivalence MC)Use the statements and truth table to determine which statements are equivalent.p: It is a fish.q: It rests at night. 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

(Logic and Truth Tables HC)Two propositional statements are given.p: All raccoons sleep during the day.q: Some raccoons stay up all night.Part A: Write a logical function to represent All raccoons sleep during the day if and only if no raccoons stay up all night. (5 points)Part B: Determine the truth table values for the column ~p ↔ q. (5 points) p q ~p ~q ~p ↔ q T T F F   T F F T   F T T F   F F T T  

(Addition and Multiplication Rules for Probability MC)A restaurant menu includes 5 types of soup, 6 types of sandwiches, 3 types of salad, and 4 types of drinks. How many different combinations of soup, sandwich, salad, and drink can a customer order?

(If…Then Statements MC)Given the statement, rewrite it as the biconditional statement p ↔ q.Statement: The cookie jar is filled with peanut butter cookies.

(Combinations and Permutations MC)A spelling bee has 21 contestants. In how many ways can they finish in first, second, and third place?

(Combinations and Permutations MC)A spelling bee has 20 contestants. In how many ways can they finish in first, second, and third place?

(Set Operations and Relations MC)Given U = {q, r, s, t, u, v, w}, A = {s, t, v, w}, and B = {r, t, v}. If A’ ∪ B’ = {q, r, s, u, w}, determine (A ∩ B)’.