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Student Name: Teacher: Date: District: Miami-Dade County Public Schools Assessment: 9_12 Mathematics Algebra II Exam 1. Form: PDF

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Student Name: Teacher: District: Date: Miami-Dade County Public Schools Assessment: 9_12 Mathematics Algebra II Exam 1 Description: Algebra 2 Topic 3 Test Form: Given the following probabilities:
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Student Name: Teacher: District: Date: Miami-Dade County Public Schools Assessment: 9_12 Mathematics Algebra II Exam 1 Description: Algebra 2 Topic 3 Test Form: Given the following probabilities: P(A) = 0.5 P(B) = 0.3 P(C) = 0.4 P(D) = 0.7 P(A and B) = 0.8 P(B and C) = 0.75 P(C and D) = 0.28 P(A and D) = 0.2 Which 2 events are independent? A and B A and D B and C C and D 2. The probability that a randomly selected American household owns at least one dog is 43%. The probability that the household owns at least one cat is 31%. The probability that the household owns either a dog or cat is 57%. What is the probability that the household owns both a cat and a dog? 12% 17% 37% 131% 3. A survey found the following results about students' favorite movie genre: Comedy Drama Horror Non-Fiction Freshman Sophomores Juniors Seniors What is the probability that someone who prefers horror, is a sophomore? There are thirty students in a class. Whether they are involved in a varsity sport or not is recorded in the table below. Varsity Sport Not in a Varsity Sport Male 12 4 Female 5 9 What is the probability a student is involved in a varsity sport given that the student is female? 5. What is the probability of getting a prime number or an even number when rolling a number cube with faces labeled 1 through 6? 6. George ordered 100 pizzas for a class party. He ordered 20 cheese pizzas, 35 pepperoni pizzas, and the rest were supreme. Isabella took the first box from the stack and noticed from the mark that it had toppings, she just couldn't tell which topping it was. Assuming that the pizzas were randomly distributed, what is the probability that she grabbed a supreme pizza? 7/20 7/16 9/20 9/16 7. Which situation involves the probability of dependent events? When a number cube is rolled two times, what is the probability of getting an even number on the second roll, given that the first was a prime number? When two number cubes are rolled, what is the probability of getting an even number on the second cube, given that the first was a prime number? What is the probability of drawing a red marble from a jar if the first marble drawn was blue, given that the marble is not replaced? What is the probability of drawing a red marble from a jar if the first marble drawn is blue, given that the marble is replaced? 8. The normal distribution curve for the points earned by 300 people on a test is shown below. How many people of the 300 who took the test earned a total number of points that fell within one standard deviation of the mean? Using the Venn diagram below, what is the complement of set A? 10. A survey was conducted to find what percentage of high school students prefer watching baseball or football or both. Students had to select one of those three options. Let A represent the set of students who prefer watching baseball and B represent the set of students who prefer watching football. Which statement correctly describes the complement of set A? The students who prefer only baseball. The students who prefer football but not baseball. The students who prefer baseball or football or both. The students who prefer only baseball or only football. 11. The table below shows the number of married and unmarried people who work in a factory. Alexandra randomly chooses a person who works in the factory. Benedict randomly chooses a male who works in the factory. Which statement best compares the probability of Alexandra choosing a married male worker versus Benedict choosing a married male worker? Both Alexandra and Benedict need to select one of the 300 married male workers, so the probabilities are equal. Alexandra has a greater probability of success, because a greater fraction of females working in the factory are married. If the female workers were less likely to be married, Benedict's probability would be higher. Benedict's experiment requires both that the condition (worker is male) and success (worker is married) be met. Alexandra has only one (compound) criterion, and is more likely to choose a married male worker. Benedict has a greater probability of success, because he is choosing from a smaller pool of workers. If there were no women working at the factory, the two probabilities would be equal. 12. Hannah rolls a standard 6 sided die two times in a row. Are the two rolls independent, and what is the probability of rolling two fives in a row? The two rolls are independent, and the probability of rolling two fives is 1/36. The two rolls are dependent, and the probability of rolling two fives is 1/36. The two rolls are independent, and the probability of rolling two fives is 1/3. The two rolls are dependent, and the probability of rolling two fives is 1/ In a school elec on four students are running for president, and five students are running for vice president. Two of the presiden al candidates are female, and three of the vice presiden al candidates are female. What is the probability that the elected president and vice president will both be male? A game of chance at a carnival involves a game spinner divided into 20 sections. The sections are colored red, blue, yellow, and green with an equal number of sections for each color. To play the game, a person pays $3 and spins the spinner twice. If it stops on the same color both times, the person wins a large stuffed animal. What is the size of the sample space for spinning the spinner twice? Which of these statements is true? The union of two sets A and B is the set of elements that are in only The union of two sets A and B is the set of elements that are in A and The union of two sets A and B is the set of elements that are in A or in B or in both. The union of two sets A and B is the set of elements that are in A or in B but not in both. 16. The table below relates the number of points scored by different basketball players in a tournament with the number of hours they spent practicing during the week before the tournament. If 50% of the basketball players scored fewer than 8 points in the tournament, what is the approximate probability that a basketball player who practiced for more than 3 hours scored fewer than 8 points? Marco is calculating the conditional probability of events A and If he determines that which statement describes events A and B? A and B are disjoint events. A and B are dependent events. A and B are independent events. A and B are complementary events. 18. The table below shows how many seniors are currently taking physics and calculus. Which expression represents the probability that a student chosen at random who is in physics will also be in calculus? 19. The students in a second grade classroom were surveyed to see if they have any pets. Of the students surveyed, 68% of them said they have a dog and 17% said they have a dog and a cat. What is the probability that a student has a cat given that the student already has a dog? 4% 17% 25% 51% 20. Amanda spins a spinner numbered 1 to 10. What is the probability that the spinner lands on an odd number or a number that is divisible by 3? 21. Katie won a large bag of candies by correctly guessing the total number of candies inside a jar. She was then given a chance to double the amount of candy she was going to receive. She was told that 20% of the candies are chocolate, 25% are hard candy, 30% are caramel and 25% are white chocolate. She is then asked the following: If I pull out a random candy, and I tell you it is not chocolate, what is the probability that it is a hard candy?' How should she respond to double her candy? 1/4 3/10 5/11 6/ A local education foundation wants to know if membership helps a student's chance of going to his first choice for college. The foundation took a random sample of local seniors who were college-bound. The results are shown below. Student Status Probability in program and accepted to 1st choice college 0.38 not in program and accepted to 1st choice college 0.17 in program and not accepted to 1st choice college 0.12 not in program and not accepted to 1st choice college 0.33 The probability of participating in the program was What is the probability a randomly selected student was accepted to the college of his choice, given that he participated in the program? 24. A survey conducted in school shows that 56% of the boys like dogs and 32% of the boys like both dogs and cats. What approximate percentage of boys like cats given that they also like dogs? 18% 24% 57% 88% 25. The heights of girls in seventh grade at eight middle schools in South County follow a normal distribution with a mean of 63.6 inches and a standard deviation of 2.7 inches. What is the approximate probability that a seventh grade South County middle school girl is taller than 5 feet 9 inches? Student Name: Teacher: District: Date: Miami-Dade County Public Schools Assessment: 9_12 Mathematics Algebra II Exam 1 Description: Algebra 2 Topic 3 Test Form: Given the following probabilities: P(A) = 0.5 P(B) = 0.3 P(C) = 0.4 P(D) = 0.7 P(A and B) = 0.8 P(B and C) = 0.75 P(C and D) = 0.28 P(A and D) = 0.2 Which 2 events are independent? MAFS.912.S-CP.1.2 A and B A and D B and C C and D 2. The probability that a randomly selected American household owns at least one dog is 43%. The probability that the household owns at least one cat is 31%. The probability that the household owns either a dog or cat is 57%. What is the probability that the household owns both a cat and a dog? MAFS.912.S-CP % 17% 37% 131% 3. A survey found the following results about students' favorite movie genre: Comedy Drama Horror Non-Fiction Freshman Sophomores Juniors Seniors What is the probability that someone who prefers horror, is a sophomore? MAFS.912.S-CP 4. There are thirty students in a class. Whether they are involved in a varsity sport or not is recorded in the table below. Varsity Sport Not in a Varsity Sport Male 12 4 Female 5 9 What is the probability a student is involved in a varsity sport given that the student is female? MAFS.912.S-CP What is the probability of getting a prime number or an even number when rolling a number cube with faces labeled 1 through 6? MAFS.912.S-CP.2.7 6. George ordered 100 pizzas for a class party. He ordered 20 cheese pizzas, 35 pepperoni pizzas, and the rest were supreme. Isabella took the first box from the stack and noticed from the mark that it had toppings, she just couldn't tell which topping it was. Assuming that the pizzas were randomly distributed, what is the probability that she grabbed a supreme pizza? MAFS.912.S-CP.2.6 7/20 7/16 9/20 9/16 7. Which situation involves the probability of dependent events? MAFS.912.S-CP.1.5 When a number cube is rolled two times, what is the probability of getting an even number on the second roll, given that the first was a prime number? When two number cubes are rolled, what is the probability of getting an even number on the second cube, given that the first was a prime number? What is the probability of drawing a red marble from a jar if the first marble drawn was blue, given that the marble is not replaced? What is the probability of drawing a red marble from a jar if the first marble drawn is blue, given that the marble is replaced? 8. The normal distribution curve for the points earned by 300 people on a test is shown below. How many people of the 300 who took the test earned a total number of points that fell within one standard deviation of the mean? MAFS.912.S-I Using the Venn diagram below, what is the complement of set A? MAFS.912.S-CP.1.1 10. A survey was conducted to find what percentage of high school students prefer watching baseball or football or both. Students had to select one of those three options. Let A represent the set of students who prefer watching baseball and B represent the set of students who prefer watching football. Which statement correctly describes the complement of set A? MAFS.912.S-CP.1.1 The students who prefer only baseball. The students who prefer football but not baseball. The students who prefer baseball or football or both. The students who prefer only baseball or only football. 11. The table below shows the number of married and unmarried people who work in a factory. Alexandra randomly chooses a person who works in the factory. Benedict randomly chooses a male who works in the factory. Which statement best compares the probability of Alexandra choosing a married male worker versus Benedict choosing a married male worker? MAFS.912.S-CP.1.5 Both Alexandra and Benedict need to select one of the 300 married male workers, so the probabilities are equal. Alexandra has a greater probability of success, because a greater fraction of females working in the factory are married. If the female workers were less likely to be married, Benedict's probability would be higher. Benedict's experiment requires both that the condition (worker is male) and success (worker is married) be met. Alexandra has only one (compound) criterion, and is more likely to choose a married male worker. Benedict has a greater probability of success, because he is choosing from a smaller pool of workers. If there were no women working at the factory, the two probabilities would be equal. 12. Hannah rolls a standard 6 sided die two times in a row. Are the two rolls independent, and what is the probability of rolling two fives in a row? MAFS.912.S-CP.1.2 The two rolls are independent, and the probability of rolling two fives is 1/36. The two rolls are dependent, and the probability of rolling two fives is 1/36. The two rolls are independent, and the probability of rolling two fives is 1/3. The two rolls are dependent, and the probability of rolling two fives is 1/ In a school elec on four students are running for president, and five students are running for vice president. Two of the presiden al candidates are female, and three of the vice presiden al candidates are female. What is the probability that the elected president and vice president will both be male? MAFS.912.S-CP A game of chance at a carnival involves a game spinner divided into 20 sections. The sections are colored red, blue, yellow, and green with an equal number of sections for each color. To play the game, a person pays $3 and spins the spinner twice. If it stops on the same color both times, the person wins a large stuffed animal. What is the size of the sample space for spinning the spinner twice? MAFS.912.S-CP Which of these statements is true? MAFS.912.S-CP.1.1 The union of two sets A and B is the set of elements that are in only The union of two sets A and B is the set of elements that are in A and The union of two sets A and B is the set of elements that are in A or in B or in both. The union of two sets A and B is the set of elements that are in A or in B but not in both. 16. The table below relates the number of points scored by different basketball players in a tournament with the number of hours they spent practicing during the week before the tournament. If 50% of the basketball players scored fewer than 8 points in the tournament, what is the approximate probability that a basketball player who practiced for more than 3 hours scored fewer than 8 points? MAFS.912.S-CP Marco is calculating the conditional probability of events A and If he determines that which statement describes events A and B? MAFS.912.S-CP.1.3 A and B are disjoint events. A and B are dependent events. A and B are independent events. A and B are complementary events. 18. The table below shows how many seniors are currently taking physics and calculus. Which expression represents the probability that a student chosen at random who is in physics will also be in calculus? MAFS.912.S-CP.1.3 Webb: The students in a second grade classroom were surveyed to see if they have any pets. Of the students surveyed, 68% of them said they have a dog and 17% said they have a dog and a cat. What is the probability that a student has a cat given that the student already has a dog? MAFS.912.S-CP.1.3 4% 17% 25% 51% 20. Amanda spins a spinner numbered 1 to 10. What is the probability that the spinner lands on an odd number or a number that is divisible by 3? MAFS.912.S-CP Katie won a large bag of candies by correctly guessing the total number of candies inside a jar. She was then given a chance to double the amount of candy she was going to receive. She was told that 20% of the candies are chocolate, 25% are hard candy, 30% are caramel and 25% are white chocolate. She is then asked the following: If I pull out a random candy, and I tell you it is not chocolate, what is the probability that it is a hard candy?' How should she respond to double her candy? MAFS.912.S-CP.2.6 1/4 3/10 5/11 6/11 22. A local education foundation wants to know if membership helps a student's chance of going to his first choice for college. The foundation took a random sample of local seniors who were college-bound. The results are shown below. Student Status Probability in program and accepted to 1st choice college 0.38 not in program and accepted to 1st choice college 0.17 in program and not accepted to 1st choice college 0.12 not in program and not accepted to 1st choice college 0.33 The probability of participating in the program was What is the probability a randomly selected student was accepted to the college of his choice, given that he participated in the program? MAFS.912.S-CP MAFS.912.S-CP A survey conducted in school shows that 56% of the boys like dogs and 32% of the boys like both dogs and cats. What approximate percentage of boys like cats given that they also like dogs? MAFS.912.S-CP % 24% 57% 88% 25. The heights of girls in seventh grade at eight middle schools in South County follow a normal distribution with a mean of 63.6 inches and a standard deviation of 2.7 inches. What is the approximate probability that a seventh grade South County middle school girl is taller than 5 feet 9 inches? MAFS.912.S-I
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