Blog

(Conditional Probability HC)A travel company tracked the preferred destinations of 225 travelers who enjoy different types of leisure activities. The data are displayed in a table. Beach Mountains City Outdor Recreation 38 21 12 Reading 32 39 18 TV/Video Games 12 23 30 Part A: Calculate the empirical conditional probability of a traveler who prefers the beach, given that they enjoy TV/video games. Show all work. (5 points)Part B: Is a traveler user more or less likely to prefer the beach if they enjoy TV/video games? Justify the answer mathematically. (5 points)

(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.

(Interpreting Independence LC)P(A) = 0.33 and P(B) = 0.44. Determine P(B|A) if events A and B are independent.

(Addition and Multiplication Rules for Probability MC)A bag contains 4 blue marbles, 6 orange marbles, and 3 yellow marbles. Select the expression that shows the probability of randomly drawing an orange marble followed by a yellow marble without replacement.

(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)’.

(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 Determine the empirical probability that a person who watched videos was an artist watching beauty tips.

(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.

(Addition and Multiplication Rules for Probability MC)A cafe offers 9 types of coffee, 3 types of tea, and 4 types of soft drinks. Determine the total number of beverages from which a customer can choose.

(Laws of Logic and Valid Arguments MC)Use the statements and truth table to determine which argument is valid.p: It rained.q: The grass is wet. Premise 1 Premise 2 Conclusion p q p → q T T T T F F F T T F F T

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