Algebra 2 Quiz 19.1 to 19.2 Review

**ALGEBRA 2 QUIZ 19.1 TO 19.2 REVIEW** 1. Set A is the set of factors of 12, set B is the set of even natural numbers less than 13, set C is the set of odd natural numbers less than 13,   set D is the set of even natural numbers less than 7. The universal set is the set of natural numbers less than 13.   A = {1, 2, 3, 4, 6, 12} B = {2, 4, 6, 8, 10, 12} C = {1, 3, 5, 7, 9, 11} D = {2, 4, 6} U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} a) What is A ∪ C? (Both sets combined - union) {1, 2, 3, 4, 5, 6, 7, 9, 11, 12} b) What is A ∩ C? (Intersection) {1, 3} c) What is U \ A? (In universal, not in A - complement) {5, 7, 8, 9, 10, 11} d) Is B ⊆ A? Explain why or why not. No, B is not a subset of A because there are elements of B that are not in A. 2. You have a set of 10 cards numbered 1 to 10. You choose a card at random. Event A is choosing a number less than 8. Event B is choosing an even number.   A = {1, 2, 3, 4, 5, 6, 7} B = {2, 4, 6, 8, 10} a) P(A) = 7/10 b) P(A ∪ B) = 9/10 3. Use the complement of the event to find the probability. You choose a card at random from a standard deck of cards. What is the probability that you do not choose a red queen? Probability of drawing a red queen:   P(red queen) = 2/52 So P(not red queen) = 1 - 2/52 = 25/26 4. Use the complement of the event to find the probability. Slips of paper numbered 1-20 are folded and placed into a hat, and then a slip of paper is drawn at   random. What is the probability the slip drawn has a number which is not a multiple   of 3 or 5? Multiples of 3 = {3, 6, 9, 12, 15, 18} Multiples of 5 = {5, 10, 15, 20} P(multiple of 3 or 5) = 9/20 P(not multiple of 3 or 5) = 1 - 9/20 = 11/20 5. You are going to roll two number cubes, a white number cube and a red number cube, and find the sum of the two numbers that come up.   What is the probability that the sum will be 9? 4/36 = 1/9 What is the probability that the sum will not be 9? 1 - 1/9 = 8/9 [Image of a 6x6 grid showing possible dice rolls and their sums] **ALGEBRA 2 QUIZ 19.1 TO 19.2 REVIEW** 6. A standard deck of cards has 13 cards (2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen, king, ace) in each of 4 suits (hearts, clubs, diamonds, spades). The hearts and diamonds cards are red. The clubs and spades cards are black.   You choose a card from a standard deck of cards at random. Event A is choosing a red card. Event B is choosing an odd number. Event C is choosing a black card. Find P(A   ∩ B ∩ C). P(A ∩ B ∩ C) = 0 because you cannot choose a card that is both black and red. 7. Nicole is trying to choose an outfit for this evening. She has narrowed her choices down to 4 pants, 5 shirts, and 4 sets of shoes. How many different outfits does Nicole have to choose   from? 4 * 5 * 4 = 80 outfits 8. An MP3 player has a playlist with 10 songs. You select the shuffle option, which plays each song in a random order without repetition, for the playlist. In how   many different orders can the songs be played?   10! = 3,628,800 9. There are 9 students on a committee. To decide which 3 of these students will attend a conference, 3 names are chosen at random by pulling names one at a time from a hat. What is the probability that Sarah, Jamal, and Mai are chosen in any order?   n(S) = 9P₃ = 504 n(A) = 3P₃ = 6 P(A) = 6/504 = 1/84 10. There are 6 female and 6 male kittens sleeping together in a row. Assuming that the arrangement is a random arrangement, what is the probability   that all the female kittens are together, and all the male kittens are together?   n(S) = 12! / (6!6!) = 924 FFFFMMM MMMMFFF 2 ways P(genders together) = 2/924 = 1/462 11. The letters G, E, O, M, E, T, R, Y are on 8 tiles in a bag, one letter on each tile. If you select tiles randomly from the bag and place them in a row from left to right, what is the probability the tiles will spell out GEOMETRY?   n(S) = 8! = 40,320 GEOMETRY 2 ways P(GEOMETRY) = 2/40,320 = 1/20,160