Quiz CHAPTER 16 NAME: UNDERSTANDING PROBABILITY AND LONG- TERM EXPECTATIONS

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1 Quiz CHAPTER 16 NAME: UNDERSTANDING PROBABILITY AND LONG- TERM EXPECTATIONS 1. Give two examples of ways that we speak about probability in our every day lives. NY REASONABLE ANSWER OK. EXAMPLES: 1) WHAT IS THE PROBABILITY OF WINNING THE LOTTERY? 2) WHAT IS THE PROBABILITY THAT YOU WILL EVENTUALLY BUY A (ANOTHER) HOUSE? 2. Which of the following chances can be quantified exactly? a. The chance that it will rain tomorrow. b. The chance that you will live to be 100. c. The chance of getting four of a kind in a poker hand. d. All of the above. 3. Give an example where you can use the relative-frequency approach to determine a probability. NY EXAMPLE WHERE THE SITUATION CAN BE REPEATED NUMEROUS TIMES AND THE OUTCOME OBSERVED EACH TIME. 4. Suppose Bob and Mary are each trying to determine whether or not a coin is fair (that is, the coin has an equal chance of landing heads up or tails up). Bob flips the coin 100 times and finds that it lands heads up 80 times. Mary flips the coin 1,000 times and finds that it lands heads up 800 times. Compare the relative frequencies in each case and discuss who (if anyone) has stronger evidence that the coin is unfair. ANSWER: MARY HAS STRONGER EVIDENCE. BOB AND MARY BOTH FOUND A RELATIVE FREQUENCY OF 0.8 OR 80%, BUT SINCE MARY S DATA IS BASED ON MANY MORE OBSERVATIONS, HERS IS MORE LIKELY TO BE CLOSE TO THE TRUE PROBABILITY THAN BOB S. 5. Describe a situation where you can t use the relative frequency approach to interpret probability. ANSWER: EITHER: 1) YOU CAN T REPEAT THE SITUATION OVER AND OVER AGAIN AND OBSERVE THE OUTCOME EACH TIME; OR 2) THE PROBABILITY KEEPS CHANGING BECAUSE OUTCOMES INFLUENCE EACH OTHER. 6. The airlines routinely report their on-time flight percentages, which can be interpreted as probabilities. What method of finding probabilities was most likely used in determining this? ANSWER: RELATIVE-FREQUENCY APPROACH; OBSERVING MANY FLIGHTS OVER TIME, AND DETERMINING WHETHER EACH ONE WAS ON TIME OR NOT.

2 7. Which of the following is not an example of using the relative-frequency interpretation of probability? a. Buying a lottery ticket every week and observing whether it is a winner. b. Testing individuals in a population and observing whether they carry a gene for a certain disease. c. Being a member of a jury and deciding that the chance of the defendant being innocent is very small. d. All of the above are examples of using the relative-frequency interpretation. 8. Suppose you encounter one traffic light on your commute to work each day. You have determined that the probability that this light will be red is 1/3. Which of the following is not a correct interpretation of this probability? a. The light will always be red one out of every three times that you encounter it. b. In the long run, the light should be red about 33.33% of the time. c. Each time you approach the light on your commute, the probability of it being red is 1/3. d. All of the above are correct interpretations. 9. Suppose you know that for each ticket the probability of winning a certain instant win lottery game is 1/100. You have purchased 99 tickets so far, with no luck. What is your chance that the next ticket you buy is a winner? a. 99/100 b. 1/100 c. 100% d. None of the above. 10. Using the relative frequency approach, we can define the probability of any specific outcome as the of times it occurs over the long run. ANSWER: PROPORTION 11. Suppose Consumer Reports tests a random sample of 1,000 flashlights of a certain brand and finds 20 of them to be defective. They report the chances of buying a defective flashlight (for this brand) to be.02. This is an example of using the approach to determining a probability. ANSWER: RELATIVE FREQUENCY 12. Name two restrictions on personal probabilities, from a statistical standpoint. ANSWER: 1) THEY MUST FALL BETWEEN 0 AND 1 (OR BETWEEN 0% AND 100%); 2) THEY MUST BE COHERENT THAT IS, YOUR PERSONAL PROBABILITIES OF TWO EVENTS CAN T CONTRADICT EACH OTHER. 13. What is one caution you should observe when encountering personal probabilities that are reported in the media? ANSWER: THEY CAN BE VERY DIFFERENT FROM PERSON TO PERSON; THEY CAN BE LESS SCIENTIFICALLY SOUND THAN THE RELATIVE FREQUENCY APPROACH. 14. Which of the following is an example of using the personal probability interpretation of probability? a. Buying a lottery ticket every week and observing whether it is a winner. b. Observing the percentage of time that all of the prices ring up correctly when you visit a certain store each week to do your shopping. c. Deciding that your football team has a high chance of winning their next game. d. All of the above are examples of using the personal probability interpretation.

3 15. Which of the following statements is not true regarding personal probabilities? a. They often take relative frequencies of similar events into account. b. They are based on unique situations that are not likely to be repeated. c. We could each assign a different personal probability to the same event. d. All of the above are true statements regarding personal probabilities. ANSWER: D 16. Which of the following is not an example of a statement based on a personal probability? a. Based on his credentials and experience, I believe this candidate has a high chance of being successful here. b. I read in a study that 98% of the patients who received this vaccine suffered no side effects, so my chances of developing side effects are very small. c. We believe beyond a reasonable doubt that the defendant is guilty. d. All of the above are statements based on personal probability. 17. Tell whether the following statement is correct; if it is not correct, explain the problem. If the probability of a single birth resulting in a boy is.51, then the probability of it resulting in a girl is also.51. ANSWER: INCORRECT; WHEN THERE ARE ONLY TWO POSSIBLE OUTCOMES, THEY MUST ADD UP TO Tell whether the following statement is correct; if it is not correct, explain the problem. 60% of the voters were in favor of Issue 1. That means 40% of them must have opposed it. ANSWER: INCORRECT; SOME VOTERS MAY HAVE BEEN NEUTRAL. Narrative: Grades Suppose a class of 100 students took their statistics final and their grades are shown in the table below. A B C D F {Grades narrative} Choose one student at random. What is the probability that he/she received a B or a C? ANSWER: 62% 20. {Grades narrative} What is the probability that a student selected at random passed the final (where a D is considered to be a passing grade)? ANSWER: 97% 21. Which of the following is a true probability? a b. 120% c. 1 d. None of the above 22. Which of the following outcomes are not mutually exclusive? a. Flip a fair coin once. Outcomes: head, tail. b. Flip a fair coin twice. Outcomes: getting at least one tail, getting at least one head. c. Flip a fair coin twice. Outcomes: getting two tails, getting two heads. d. All of the above pairs of outcomes are mutually exclusive.

4 23. Suppose the outcomes of births within a given family are independent of each other, and a couple has already had four boys. Which of the following best describes the probability that their next baby will be a girl? a. Approximately 50% b. Much less than 50% c. Much greater than 50% d. Not enough information to tell 24. Suppose your commute to work involves encountering 3 intersections in town and then getting on the Interstate for 10 miles. Your driving experiences in town and on the Interstate are unrelated. Suppose your chances of hitting a red light in town are 1 in 10, and your chances of getting tied up in traffic on the Interstate are 2 in 10. What are the chances of having both happen on the same trip to work? a. 3/10 =.30 or 30% b. 2/100 =.02 or 2% c. 3/20 =.15 or 15% d. None of the above 25. Suppose the chance that your plane will depart and arrive on time in the same trip is 90%. The chance that your plane will depart on time on any given trip is 90%. (Choose one: at most, equal to, or at least, and fill in the blank.) T LEAST 26. If two events are mutually exclusive, they be independent. ANNOT Narrative: Shaking hands Suppose the chances of picking up a cold from someone by shaking hands with them is.01 (assuming you don t know whether they have a cold or not), and that each encounter you have is independent of another. 27. {Shaking hands narrative}. Suppose you shake hands with 5 people in a given day. What is the probability that you don t pick up a cold from any of these people? ANSWER:.95, FOUND AS (.99) {Shaking hands narrative} Explain, using probability, why your chance of not getting a cold in a given day decreases as the number of handshakes you make increases? ANSWER: THE CHANCE OF NOT GETTING A COLD IS.99 FOR EACH ENCOUNTER AND YOU HAVE TO MULTIPLY BY.99 FOR EACH SUBSEQUENT HANDSHAKE. SINCE.99 < 1, THIS MAKES THE OVERALL PROBABLY GO DOWN MORE EACH TIME. 29. Which probability is the smallest? a. The probability that a couple s third child is a girl. b. The probability that a couple has their first girl by the time of the third child. c. The probability that a couple s first girl occurs the third time around. d. All of the above probabilities are equal.

5 Narrative: Instant lotto Suppose an Instant Lotto ticket costs $5, and the chances of winning the $500 prize are 1/10,000. There are no other prizes. 30. {Instant lotto narrative} What is your expected value for this game for each ticket you buy? ANSWER: -$ {Instant lotto narrative} Interpret what the expected value would mean in this situation, in words that a non-statistics student would understand. (It is not necessary to calculate the expected value here.) ANSWER: OVER MAY REPETITIONS OF THIS GAME, YOU WILL LOSE AN AVERAGE OF $4.95 EACH TIME YOU PLAY. Narrative: Taxes Suppose you have a taxing policy where 60% of the population pays $10,000 per year in taxes per person, and the other 40% pays $100 per year in taxes per person. 32. {Taxes narrative} What is the expected value for the amount of yearly taxes paid by one person in this population? ANSWER: $6, {Taxes narrative} Explain how the expected value can be misleading if it is interpreted by someone as the amount of taxes they will have to pay in a given year. ANSWER: THE EXPECTED VALUE IS AN OVERALL AVERAGE AMOUNT, AND DOES NOT APPLY IN THIS CASE TO ANY SINGLE MEMBER OF THE POPULATION; THEY LL EITHER PAY $100 OR $10, Which of the following describes an example of an expected value in a lottery situation? a. The average amount of money you ll win/lose in the long run when playing the lottery. b. The amount of money you will win/lose on any given ticket. c. The amount of money that you ll have the highest chances of winning. d. All of the above. 35. Suppose 5% of the people who buy a certain type of DVD player return it to get their money back. The DVD player costs $100. What is the expected loss, per customer, for the company due to returns (ignoring the monetary value of the returned DVD player)? a. $5 b. $0; most people don t return it c. Either $0 or $100, but it is impossible to determine which. d. $ Suppose a slot machine has an expected payout of.95 cents on the dollar, meaning for every dollar you play, you get 95 cents back. What is your expected value for the amount lost per dollar played on this machine? a. $0.95 b. -$0.05 c. -$1.00 d. The entire jackpot, if you play long enough.

6 37. Suppose 40% of the people in a population smoke 20 cigarettes per day, and the remaining 60% smoked none. Which of the following involves a correct interpretation of the expected value? a. For all people in the population, the average is 8 cigarettes smoked per person per day. b. For all people in the population, the average is 20 cigarettes smoked per person per day. c. The chance is high that the next person you meet smokes eight cigarettes a day. d. Almost everyone in the population smokes close to eight cigarettes per day. 38. The represents the average value of any measurement over the long run. ANSWER: EXPECTED VALUE 39. The expected value have to be one of the possible outcomes. (Choices: does or does not. ) ANSWER: DOES NOT