Test Date: A. Get none of the 5 questions correct. B. Get all of the questions wrong. C. Get at least one question wrong

Transcription

1 Review! Probability Chapter Complete each problem in the seconds column. Record answers to the side questions in the 2nd column completely. Name: Test Date: Class: AP Statistics Period : Chapter 14: From Randomness to Probability Review What does disjoint mean in terms of probability? 1. Five multiple choice questions, each with four possible answers, appear on your next quiz. What is the probability that if you just guess (no preparation), you... A. Get none of the 5 questions correct B. Get all of the questions wrong C. Get at least one question wrong How can you determine if a probability model is legitimate? D. Get your first incorrect answer on the fourth question E. Explain why this scenario has disjoint events. 2. After picking 10 M&M s in a row, you still have not picked a red one! Syed said that you should have a better chance of getting a red candy on your next pick since you have yet to see one. Comment on his statement. Explain why when you see at least you can use the complement rule. (Hint: Look back at the tossing 3 coins example in your notes) 3. Academy Sports and Outdoors announces a Wheel of Savings sale. Customers select the merchandise they want to purchase, then at the cash register spin a wheel to determine the size of the discount they get. The wheel is divided into 12 regions of equal size. Size of the regions are 10%, 3 are 20%, 2 are 40%, and the last space is 100% discount - means they don t pay anything! Find the probability that... A. A customer gets a least a 40% discount? Define probability in your own words. B. Two customers in a row get only 10% discounts? C. Three consecutive customers get all 20% discounts? D. None of the first four customers get a discount over 20%? E. There is at least one 100% winner among the first six customers? Page 1

2 4. You start flipping a coin to pass the time waiting at the DMV. The person next to you says that your coin must be weighted because it keeps landing on heads. How would you respond to his reasoning? What must be true about the values of probabilities? Explain why you think people believe in the Law of Averages. Multiple Choice Practice: 4. Which of the following is a TRUE statement? A. An event that is certain not to happen has a probability of 1.0 B. Probabilities are numbers that range from -1 to 1. C. The total of the probabilities assigned to all outcomes in a sample space must be exactly 1.0. D. Probabilities are always integers. E. If two events are disjoint, then they must share at least one outcome. Review the following keywords: Event Complement Sample Space Probability Model Disjoint Probability Independent Mutually Exclusive 5. Jacob and Lauyrn are scheduled to take their midterm in Statistics. The probability that Jacob will pass is The probability that Lauryn will pass is If the two events are independent (i.e. Jacob passing does NOT affect her passing), which statement is correct? A. The probability that exactly one passes is B. The probability that exactly one fails is C. The probability that they both pass is D. The probability that both pass is 1.0. E. The probability that both fail is Heights of the average teenage male at RHS are approximately Normal with the mean height being 66 inches and a standard deviation of 4.5 inches. What percentage of males do we expect to be taller than 6 feet? Sketch a Normal model to support your work. Don t forget about the Normal distributions from previous material! These were probabilities :) SUmmary: Explain the difference between law of large numbers and law of averages. Page 2

3 7. Suppose the probability that a construction company will be awarded a certain contract is.25, the probability that it will be awarded second contract is.21, and the probability that it will get both contracts is.13. What is the probability that the company will win at least one of the two contracts? 8. Assume that X and Y are events in the same sample space. If P(X) = 0.30 and P(Y)=0.75 then which of the following inequalities MUST be true? I. P(X and Y) 0.05 II. P(X and Y) 0.35 III. P(X and Y) 0.30 (A) I and II (B) I and III (C) II and III (D) II only (E) I, II, III Chapter 15: Probability Rules Review How can you decide whether two events are independent? 7. A survey of families revealed that 58% of all families eat turkey at holiday meals, 44% eat ham, and 16% have BOTH ham and turkey at holiday meals. Calculate the following probabilities. A. Create a Venn diagram to model this scenario. Explain why the General Addition Rule works for events that are NOT disjoint. B. A randomly selected family had neither turkey nor ham. Remember: Or in probability means that BOTH can occur. For example: Do you want cream or sugar in you coffee? You can have both! C. A randomly selected family had only ham without having turkey. D. A randomly selected family having turkey had ham at their holiday meal. E. Are having ham and having turkey disjoint events? Explain. Page 3

4 Explain how mutually exclusive and independent are different? 8. A survey of local car dealers revealed that 64% of all cars sold last month had a USB adapter, 28% ha alarm systems, and 22% had both USB adapters and alarms. What is the probability that A. Construct a Venn Diagram of this scenario to help you. Can disjoint events be independent? Explain. B. One of these cars selected at random had neither an adapter nor an alarm. C. That a car had a USB adapter unprotected by an alarm system. D. A car with an alarm system had a USB adapter? Explain how replacement and without replacement can change your probabilities. E. Are having an adapter and an alarm system disjoint events? Explain. Can you reverse conditional probabilities? Explain. 9. For the purpose of making budget plans for staffing, a college reviewed student s year in school and area of study. Of the students, 22.5% are seniors, 25% are juniors, 25% are sophomores, and the rest are freshmen. Also, 40% of the seniors major in the area of humanities, as did 39% of the juniors, 40% of the sophomores, and 36% of the freshmen. What is the probability that a randomly selected humanities major is a junior? 10. You draw a card from a standard deck of 52 cards that have been shuffled. Find each of the following probabilities. A. The card is black, given that it s a king. Given two diagrams that can help you determine probabilities. Explain the advantage and disadvantages of both diagrams. B. The card is red, given that it is a diamond. C. The card is an ace or a heart. D. The card is an face card or a club Page 4

5 Multiple Choice Practice: 11. Suppose A and B are given the following probabilities: P(A)=0.62 and P(B)=0.44 and P(A and B) = Which of the following conclusions can be drawn from the data? You will be given the following 2 formulas: General Addition Rule Conditional Probability The rest you MUST remember. A. P(A or B) = 0.75 B. A and B are mutually exclusive events. C. A and B are independent events. D. P(A given B) cannot be determined from the information. E. P(B given A) cannot be determined from the information. 12. Suppose A and B are given the following probabilities: P(A)=0.54 and P(B)=0.20, and P(A and B) = Which of the following conclusions can be drawn? A. A and B are mutually exclusive events. B. A and B are independent events. C. A and B are dependent events. D. A and B are complementary events. E. Not enough information is given to draw a conclusion. 13. Three machines are used to fill bottles of soda. Machines A, B, and C, fill 60%, 30% and 10% of the bottles, respectively. Of those bottles filled by Machines A, B and C, 1 percent, 2 percent and 5 percent, respectively, are underfilled. Find the probability that a bottle of soda will be underfilled. 14. A manufacturer of a premium ice cream used 2 machines to fill pint containers of its best seller - super chocolate almond fudge. Each pint is supposed to have 38 almonds, but 25 percent of the time the older machine will dispense fewer, while this occurs only 10 percent of the time with the newer machine. Eighty percent of all packages are filled by the newer machine. a.) What proportion of super almond fudge pints contain fewer than 38 almonds? b.) Suppose after a difficult exam you reward yourself and purchase a pint of this ice cream, and you find that it contains fewer than 38 almonds. What is the probability that the container was filled by the older machine? Don t forget! Your textbook has additional problems with ODD answers in the back of the book!! Page 5