Name: Class: Date: ID: Mod 2 Test Review GEO Multiple Choice Identify the choice that best completes the statement or answers the question.. Let U be the set of all integers from to 20. Let = {, 3, 6, 9, 2, 5, 8} and B = {, 6, 2, 8}. Which choice describes the set given below? {2, 4, 5, 7, 8, 0,, 3, 4, 6, 7, 9, 20} 4. You spin the numbered spinner shown below. Event is landing on a prime number. Event B is landing on an odd number. What is the intersection of and B? B C D B B B B 2. Let U be the set of all integers from to 20. Let = {, 3, 6, 9, 2, 5, 8} and B = {2, 9,, 20}. Which choice describes the set {4, 5, 7, 8, 0, 3, 4, 6, 7, 9}? B B B C B D B 3. If P 0.36, what is P? 0.06 B 0.54 C 0.60 D 0.64 E 0.72 B {3, 5, 7} C {, 2, 3, 5, 7} D {, 2, 3, 4, 5, 6, 7, 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? 0.2 B 0.5 C 0.74 D 0.8
Name: ID: 6. Darren randomly chooses a card from a standard deck of playing cards. What is the probability that Darren chooses a club or a queen? 4 B 3 C 6 D 7 Numeric Response. ccording to the Small Business dministration, 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 nswer. Suppose you roll two fair number cubes. You want to know the pairs of numbers that will result in an odd product less than 0. a. Complete the table to show the sample space for the product of the two numbers on the number cubes. 2 3 4 5 6 2 4 3 9 4 6 5 25 6 36 b. Find the subset 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 0. 2. 6 cards numbered through 6 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 0? Show your work. 3. box contains 00 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. Stars No stars Total Red 0 65 65 Black 0 25 35 Total 0 90 00 4. bank assigns random 4-digit numbers for TM access codes. In each code, no digit is repeated. Use combinations to find the number of ways that 4 digits can be chosen from 0 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. 2
Name: ID: 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 Male 2 35 Female 6 36 6. There are 7 singers competing at a talent show. In how many different ways can the singers appear? 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? 8. Thirteen people are entered in a race. If there are no ties, in how many ways can the first three places be awarded? 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. Travis s collection of DVDs contains 4 comedies, 2 dramas, and 0 action movies. Use combinations to find the probability of each of the following compound events, and then order the events, B, C, and D from least likely to most likely. Event : 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
Mod 2 Test Review GEO nswer Section MULTIPLE CHOICE. NS: C PTS: DIF: DOK 2 NT: S-CP.. ST: S-CP. TOP: pply Set Theory KEY: probability complement 2. NS: C PTS: DIF: DOK 2 NT: S-CP.. ST: S-CP. KEY: probability complement 3. NS: B PTS: DIF: DOK NT: S-CP.. ST: S-CP. 4. NS: B The possible outcomes are {, 2, 3, 4, 5, 6, 7, 8}. {2, 3, 5, 7} B {, 3, 5, 7} The intersection of and B contains the elements that are both in set and in set B. B {3, 5, 7} Feedback The intersection of and B contains the elements that are both in set and in set B. There are elements in this set. B That s correct! C You found the union of and B, not the intersection of and B. D You found the sample space. PTS: DIF: DOK NT: S-CP..* MP.4 ST: S-CP.* MP.4 KEY: outcomes subset intersection 5. NS: C PTS: DIF: DOK 2 NT: S-CP.B.7 ST: S-CP.7 6. NS: C P(club) 3 ; P(queen) 4 ; P(club and queen) Use the addition rule: P(club or queen) P(club) P(queen) P(club and queen) 3 4 6 B C D 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: DIF: DOK NT: S-CP.B.7* MP.4 ST: S-CP.7* MP.4 KEY: addition rule probability
NUMERIC RESPONSE. NS: 56% PTS: DIF: DOK NT: S-CP.. ST: S-CP. LOC: 2.4.4.h KEY: complementary probability SHORT NSWER. NS: a. 2 3 4 5 6 2 3 4 5 6 2 2 4 6 8 0 2 3 3 6 9 2 5 8 4 4 8 2 6 20 24 5 5 0 5 20 25 30 6 6 2 8 24 30 36 b. {(, ), (, 3), (, 5), (3, ), (3, 3), (3, 5), (5, ), (5, 3), (5, 5)} c. B {(, ), (, 3), (, 5), (3, ), (3, 3), (5, )} a. point b. 2 points c. 2 points PTS: 5 DIF: DOK 2 NT: S-CP..* MP.4 ST: S-CP.* MP.4 KEY: outcomes sample space subset 2. NS: P(less than 5) 4 6 ; P(greater than 0) 6 6 ; P(less than 5 and greater than 0) 0 6 P(less than 5 or greater than 0) 4 6 6 6 0 6 0.625 point for answer; 2 points for work PTS: 3 DIF: DOK 2 NT: S-CP.B.7* MP.4 ST: S-CP.7* MP.4 KEY: addition rule probability 2
3. NS: The probability is. P(black) 35 90 25 ; P(no stars) ; P(black and no stars) 00 00 00 P(black or no stars) 35 00 90 00 25 00 00 00 ny randomly selected ball will either be black or not have stars on it. point for answer; point for justification PTS: 2 DIF: DOK 2 NT: S-CP.B.7* MP.4 ST: S-CP.7* MP.4 KEY: addition rule probability 4. NS: 0! There are 0 C 4 4! (0 4)! 0 9 8 7 20 combinations of 4 digits. 4 3 2 The probability of being assigned a code with the digits 6, 7, 8, and 9 is 20. point for number of combinations; point for probability; point for work PTS: 3 DIF: DOK NT: S-CP.B.9(+)* MP.4 ST: S-CP.9(+)* MP.4 KEY: combinations probability compound events 5. NS: 7 PTS: DIF: DOK NT: S-CP..4 ST: S-CP.4 TOP: Find Probabilities of Independent and Dependent Events KEY: conditional probability 6. NS: 5,040 ways PTS: DIF: DOK OBJ: Finding Permutations NT: S-CP.B.9 ST: S-CP.9 LOC: MTH.C.3.06.02.02.004 TOP: Permutations and Combinations KEY: permutation ordering 7. NS: 5 6 PTS: DIF: DOK NT: S-CP.. ST: S-CP. 8. NS: 76 PTS: DIF: DOK NT: S-CP.B.9 ST: S-CP.9 TOP: Permutations KEY: permutation 3
9. NS: 0.56 PTS: DIF: DOK 2 NT: S-CP.B.9 ST: S-CP.9 PROBLEM. NS: There are 4 2 0 36 DVDs, and 36 36! 36 35 34 740 different ways to pick 3 DVDs. 3! (36 3)! 3 2 4! 4 3 2 : There are 4 364 different ways to pick 3 of the 4 comedies. 3! (4 3)! 3 2 The probability of randomly selecting 3 comedies is 364 740 3 255. 2! 2 0 B: There are 2 220 different ways to pick 3 of the 2 dramas. 3! (2 3)! 3 2 The probability of randomly selecting 3 dramas is 220 740 357. 0! C: There are 0 3! (0 3)! 0 9 8 20 different ways to pick 3 of the 0 action movies. 3 2 The probability of randomly selecting 3 action movies is 20 740 2 9. 24! 24 23 22 D: There are 24 2024 different ways to pick 3 of the 24 movies that are not 3! (24 3)! 3 2 dramas. The probability of randomly selecting 3 movies that are not dramas is 2024 740 506 785. In order from least likely to most likely: C, B,, D.5 points for each probability and work involving combinations; point for correct order PTS: 7 DIF: DOK 3 NT: S-CP.B.9(+)* MP.4 ST: S-CP.9(+)* MP.4 KEY: combinations probability compound events 4