Chapter 17 Solutions and Mini-Project Notes

CHAPTER 17 SOLUTIONS AND MINI-PROJECT NOTES

CHAPTER 17 PSYCHOLOGICAL INFLUENCES ON PERSONAL PROBABILITY EXERCISE SOLUTIONS

17.1 The pseudocertainty effect applies to situations where the risk is reduced to zero for only a subset of possibilities and is not affected at all for the others.

17.2 Anchoring is used. You anchor on the higher values and think they are normal, so the price of $16.99 sounds really good.

17.3 The availability heuristic is responsible because mosquitoes are more likely to bother people, and many of the termites are in unpopulated areas.

17.4 a. The events in the second statement are a subset of the first. From Rule 4 in Chapter 16, we know that the probability of a subset of events cannot be higher than the probability of the full set. (Notice that personal probabilities are relevant here, but the rules should still apply.) b. They are likely to assign higher probability to statement B because of the excess detail. It is more representative of how people think such things could happen.

17.5 Bringing to mind a detailed, plausible scenario will increase your personal probability of it happening. An example is someone trying to sell you a car alarm by describing in detail the methods thieves use.

17.6 The solicitor was using "anchoring" by trying to anchor donors on the high value of $300. The resulting donations would probably be higher than they would be if the solicitor has said "we typically get donations of $25 to $50, how much can you give?"

17.7 The availability heuristic tells us that people assign higher probabilities to events they can readily bring to mind. By listing reasons why you might be wrong, you are actually bringing them to mind, and thus are likely to assign a higher probability to the notion that you might be wrong.

17.8 The reason is the availability heuristic. Deaths from accidents are more readily brought to mind because they get more media attention. (Also, younger people are more likely to know people who have died from accidents and most of these studies are done using students.)

17.9 Statement A has a higher probability because the ways in which statement B can happen are a subset of those for statement A. But many people would think statement B had a higher probability because it is representative of what people think would happen.

17.10 a. Anchoring involves fixing a value in your mind first, then discussing the question of interest. So, for example, the salesperson might tell you what other companies could be charging, then give you their rates (lower, of course). Or, the person might ask you something like "Do you think your risk of needing this insurance is higher or lower than 90%?" thus fixing the idea that you are very likely to need insurance, without actually lying to you. b. Pseudocertainty involves the idea of convincing you that your risk of certain problems will be zero, without mentioning that other problems are not covered at all. For example, the salesperson might tell you that you are completely covered for x, y and z mishaps, and doesn't that give you peace of mind? You are not told that you are not covered at all for a, b and c mishaps. c. Availability is the idea that you will increase your personal-probability estimate of something that can readily be brought to mind. So the salesperson would try to get you to imagine what terrible things could happen to you. It could be done by saying something like, "Did you see that terrible accident in the news last week? It can happen to anybody!" Or, "Do you know anyone who died young and left a young family with no life insurance? Imagine what would happen to your wife and kids!"

17.11 People use the fact that there are 5 billion people in the world as an anchor; even if the estimate is not given they know there are billions of people. So they picture a very large container and do not adjust for the fact

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that a cube has the width multiplied by itself three times. (Notice that a width of 870 feet results in a volume of 8703 cubic feet, which is about 670 million cubic feet, which holds about 5 billion gallons of blood.)

17.12 The availability heuristic applies to this situation. The extensive media coverage of the few major airline accidents that have occurred raises people's perception of the risk.

17.13 a. The availability heuristic applies, because deaths by shark are big news and have even been the subject of movies. When did you last see a movie in which someone was killed by falling airplane parts? b. The representative heuristic would come into play. It is consistent with most people's views of the world to think that wanting desperately to get into medical school would lead someone to fight hard to get good grades. Being given a possible explanation that is representative of how they see the world might thus lead the jurors to give the explanation high probability. c. Availability is responsible. It is much easier to bring to mind words that start with k, by making the sound and seeing what follows, than it is to think of words with k as the third letter. d. This is caused by being overly optimistic. Most people in their 40s do not think they are about to die.

17.14 You should ask about the base rate or probability for people like you, and the probabilities of false positives and false negatives (or the sensitivity and specificity).

17.15 a. Conservatism might lead a smoker to ignore accumulating evidence that the smoke from their cigarettes harms those around them. b. Optimism might lead one to drive after drinking, thinking they won't have an accident or get caught. c. Forgotten base rates might make someone panic when they learn they have tested positive for a rare disease. d. Availability may lead one to think crime is much more prevalent than it really is, since it is so often featured in the news.

17.16 Optimism, because people think they will be the lucky winner. Availability might apply because there is sometimes extensive media coverage of winners.

17.17 You could determine this by noting what percentage of the time a person gets an A in a class when she has predicted it with probability 0.10 and do the same for her predictions with probability 0.90. If she is perfectly calibrated, then it will occur in 10% of the cases for which she predicted it with probability 0.10 and in 90% of the cases for which she predicted it with probability 0.90.

17.18 The probability is 0.353:

No. of People Probability of Match Accumulated Probability 1 1/12 1/12 = 0.0833 2 (11/12)(1/12) 11/144 + 1/12 = 0.16 3 (11/12)2(1/12) (11/12)2(1/12)+0.16 = 0.23 4 (11/12)3(1/12) (11/12)3(1/12)+0.23 = 0.294 5 (11/12)4(1/12) (11/12)4(1/12)+0.294 = 0.353

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NOTES ABOUT THE MINI-PROJECTS FOR CHAPTER 17

Mini-Project 17.1 Make sure the study was carried out using the ideas from Part 1 of the book. The wording should be as unbiased as possible. The sample size should be large enough to see the desired effect. Beyond that, there is substantial scope for this project.

Mini-Project 17.2 One possibility is a form of anchoring in which a store will announce a competitor's prices. However, the pseudocertainty type of idea applies because they will announce prices only for certain products, namely, the ones for which they charge less. Another possibility is presenting a detailed picture of how you would use the item, such as when trying to sell a swimming pool or hot tub and people are pictured having fun in one. Yet another possibility is to take advantage of optimism, such as when trying to sell an investment opportunity and explaining how rich you could become if you buy.

Mini-Project 17.3 There are a multitude of possibilities for this project and it is not possible to anticipate all of the responses.

Mini-Project 17.4 This project is designed to help understand the meaning of a personal probability and of calibration. The event in question should be one for which the relative-frequency probability would not be known in advance, yet for which the event is repeatable throughout the week. To be well calibrated, the proportion of times the event occurred out of the possible opportunities for it to occur should be close to the assigned personal probability. For example, suppose you estimate that you will have to stop about 40% of the time when you encounter a traffic light on your commute. Then you should count the number of times you have to stop, and divide by the number of traffic lights you pass. If that proportion is close to 40%, you are well calibrated.