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Name: ________________________ Class: ___________________ Date: __________ ID: A Mod 21 Test Review GEO Multiple Choice Identify the choice that best completes the statement or answers the question. 4. You spin the numbered spinner shown below. Event A is landing on a prime number. Event B is landing on an odd number. What is the intersection of A and B? 1. Let U be the set of all integers from 1 to 20. Let A = {1, 3, 6, 9, 12, 15, 18} and B = {1, 6, 12, 18}. Which choice describes the set given below? {2, 4, 5, 7, 8, 10, 11, 13, 14, 16, 17, 19, 20} A B C D AB AB AB AB 2. Let U be the set of all integers from 1 to 20. Let A = {1, 3, 6, 9, 12, 15, 18} and B = {2, 9, 11, 20}. Which choice describes the set {4, 5, 7, 8, 10, 13, 14, 16, 17, 19}? A AB B AB C AB D AB 3. If P A 0.36 , what is P A ? A 0.06 B 0.54 C 0.60 D 0.64 E 0.72 A B C D {3, 5, 7} {1, 2, 3, 5, 7} {1, 2, 3, 4, 5, 6, 7, 8} A B C D 0.2 0.5 0.74 0.8 5. Of 50 students going on a class trip, 35 are student athletes and 5 are left-handed. Of the student athletes, 3 are left-handed. Which is the probability that one of the students on the trip is an athlete or is left-handed? 1 Name: ________________________ ID: A 6. Darren randomly chooses a card from a standard deck of 52 playing cards. What is the probability that Darren chooses a club or a queen? A B C D 4 52 13 52 16 52 17 52 Numeric Response 1. According to the Small Business Administration, the probability that a newly started business will last four years is 44%. What is the probability that a newly started business will NOT last four years? Short Answer 1. Suppose you roll two fair number cubes. You want to know the pairs of numbers that will result in an odd product less than 10. a. Complete the table to show the sample space for the product of the two numbers on the number cubes. 1 2 3 4 5 6 1 1 2 4 3 9 4 16 5 25 3. A box contains 100 small rubber balls. The table below shows how many balls are red, how many are black, how many have stars, and how many do not have stars. What is the probability that a randomly selected ball is black or does not have stars on it? Justify your answer. 6 Red Black Total 36 Stars 0 10 10 No stars 65 25 90 Total 65 35 100 4. A bank assigns random 4-digit numbers for ATM access codes. In each code, no digit is repeated. Use combinations to find the number of ways that 4 digits can be chosen from 10 digits, if order is not important. What is the probability that Edmond is assigned a code with the digits 6, 7, 8, and 9 in any order? Show your work. b. Find the subset A of the sample space that describes two numbers with an odd product. c. Find the subset B of your answer from part a that describes an odd product less than 10. 2. 16 cards numbered 1 through 16 are placed face down and Stephanie chooses one at random. What is the probability that the number on Stephanie’s card is less than 5 or greater than 10? Show your work. 2 Name: ________________________ ID: A 5. The table shows the distribution of male and female students and left- and right-handed students in the math club. Find the probability that a female student selected at random is left-handed. Express your answer as a fraction in simplest form. Left-handed Right-handed 2 35 Male 6 36 Female 6. There are 7 singers competing at a talent show. In how many different ways can the singers appear? 8. Thirteen people are entered in a race. If there are no ties, in how many ways can the first three places be awarded? 7. Caleb and Drew are playing a game with a pair of dice. Caleb needs a sum of 5 or greater to win. What is his probability of winning on his next turn? 9. 6 high school seniors choose from among 20 quotes for their yearbook. What is the probability that at least 2 of them choose the same quote? Problem 1. Travis’s collection of DVDs contains 14 comedies, 12 dramas, and 10 action movies. Use combinations to find the probability of each of the following compound events, and then order the events A, B, C, and D from least likely to most likely. Event A: Event B: Event C: Event D: Randomly selecting 3 comedies Randomly selecting 3 dramas Randomly selecting 3 action movies Randomly selecting 3 movies that are not dramas 3 ID: A Mod 21 Test Review GEO Answer Section MULTIPLE CHOICE 1. ANS: C PTS: 1 DIF: DOK 2 NAT: S-CP.A.1 STA: S-CP.1 TOP: Apply Set Theory KEY: probability | complement 2. ANS: C PTS: 1 DIF: DOK 2 NAT: S-CP.A.1 STA: S-CP.1 KEY: probability | complement 3. ANS: B PTS: 1 DIF: DOK 1 NAT: S-CP.A.1 STA: S-CP.1 4. ANS: B The possible outcomes are {1, 2, 3, 4, 5, 6, 7, 8}. A {2, 3, 5, 7} B {1, 3, 5, 7} The intersection of A and B contains the elements that are both in set A and in set B. A B {3, 5, 7} A B C D Feedback The intersection of A and B contains the elements that are both in set A and in set B . There are elements in this set. That’s correct! You found the union of A and B, not the intersection of A and B. You found the sample space. PTS: STA: 5. ANS: STA: 6. ANS: 1 DIF: DOK 1 NAT: S-CP.A.1* | MP.4 S-CP.1* | MP.4 KEY: outcomes | subset | intersection C PTS: 1 DIF: DOK 2 NAT: S-CP.B.7 S-CP.7 C 13 4 1 P(club) ; P(queen) ; P(club and queen) 52 52 52 Use the addition rule: P(club or queen) P(club) P(queen) P(club and queen) A B C D 13 4 1 16 52 52 52 52 Feedback You found the probability that Darren chooses a queen. You found the probability that Darren chooses a club. That’s correct! Do not count the queen of clubs twice. PTS: 1 DIF: STA: S-CP.7* | MP.4 DOK 1 NAT: S-CP.B.7* | MP.4 KEY: addition rule | probability 1 ID: A NUMERIC RESPONSE 1. ANS: 56% PTS: 1 LOC: 12.4.4.h DIF: DOK 1 NAT: S-CP.A.1 KEY: complementary | probability STA: S-CP.1 SHORT ANSWER 1. ANS: a. 1 2 3 4 5 6 1 1 2 3 4 5 6 2 3 4 5 2 3 4 5 4 6 8 10 6 9 12 15 8 12 16 20 10 15 20 25 12 18 24 30 6 6 12 18 24 30 36 b. A {(1, 1), (1, 3), (1, 5), (3, 1), (3, 3), (3, 5), (5, 1), (5, 3), (5, 5)} c. B {(1, 1), (1, 3), (1, 5), (3, 1), (3, 3), (5, 1)} Rubric a. 1 point b. 2 points c. 2 points PTS: 5 DIF: DOK 2 NAT: S-CP.A.1* | MP.4 STA: S-CP.1* | MP.4 KEY: outcomes | sample space | subset 2. ANS: 4 6 0 P(less than 5) ; P(greater than 10) ; P(less than 5 and greater than 10) 16 16 16 4 6 10 P(less than 5 or greater than 10) 0.625 16 16 16 Rubric 1 point for answer; 2 points for work PTS: 3 DIF: STA: S-CP.7* | MP.4 DOK 2 NAT: S-CP.B.7* | MP.4 KEY: addition rule | probability 2 ID: A 3. ANS: The probability is 1. 35 90 25 P(black) ; P(no stars) ; P(black and no stars) 100 100 100 35 90 25 100 P(black or no stars) 1 100 100 100 100 Any randomly selected ball will either be black or not have stars on it. Rubric 1 point for answer; 1 point for justification PTS: 2 DIF: DOK 2 NAT: S-CP.B.7* | MP.4 STA: S-CP.7* | MP.4 KEY: addition rule | probability 4. ANS: 10! 10 9 8 7 210 combinations of 4 digits. There are 10 C 4 4! (10 4)! 4321 1 The probability of being assigned a code with the digits 6, 7, 8, and 9 is . 210 Rubric 1 point for number of combinations; 1 point for probability; 1 point for work PTS: 3 DIF: STA: S-CP.9(+)* | MP.4 5. ANS: 1 7 DOK 1 NAT: S-CP.B.9(+)* | MP.4 KEY: combinations | probability | compound events PTS: 1 DIF: DOK 1 NAT: S-CP.A.4 TOP: Find Probabilities of Independent and Dependent Events 6. ANS: 5,040 ways STA: S-CP.4 KEY: conditional | probability PTS: 1 DIF: DOK 1 NAT: S-CP.B.9 STA: S-CP.9 TOP: Permutations and Combinations 7. ANS: 5 6 OBJ: Finding Permutations LOC: MTH.C.13.06.02.02.004 KEY: permutation | ordering PTS: 1 8. ANS: 1716 DIF: DOK 1 NAT: S-CP.A.1 STA: S-CP.1 PTS: 1 DIF: TOP: Permutations DOK 1 NAT: S-CP.B.9 KEY: permutation STA: S-CP.9 3 ID: A 9. ANS: 0.56 PTS: 1 DIF: DOK 2 NAT: S-CP.B.9 STA: S-CP.9 PROBLEM 1. ANS: There are 14 12 10 36 DVDs, and 36 C3 36! 36 35 34 7140 different ways to pick 3 DVDs. 3! (36 3)! 321 14! 14 13 12 364 different ways to pick 3 of the 14 comedies. 3! (14 3)! 321 364 13 The probability of randomly selecting 3 comedies is . 7140 255 12! 12 11 10 220 different ways to pick 3 of the 12 dramas. B: There are 12 C 3 3! (12 3)! 321 220 11 The probability of randomly selecting 3 dramas is . 7140 357 10! 10 9 8 120 different ways to pick 3 of the 10 action movies. C: There are 10 C 3 3! (10 3)! 321 120 2 The probability of randomly selecting 3 action movies is . 7140 119 24! 24 23 22 2024 different ways to pick 3 of the 24 movies that are not D: There are 24 C 3 3! (24 3)! 321 dramas. 2024 506 The probability of randomly selecting 3 movies that are not dramas is . 7140 1785 A: There are 14 C3 In order from least likely to most likely: C, B, A, D Rubric 1.5 points for each probability and work involving combinations; 1 point for correct order PTS: 7 DIF: STA: S-CP.9(+)* | MP.4 DOK 3 NAT: S-CP.B.9(+)* | MP.4 KEY: combinations | probability | compound events 4