Here is a link to all the clicker slides.
Exam is Thursday at 12:45. Bring a Scantron 882-E and your calculator.
As noted in class, exam will consist of a selection of the Kahneman slides, problems from the two previous tests, and a few new problems similar to those on the other tests.
Read TFS 38!
Read TFS 37 and IPIL 13.
Also, please do the class evaluation. To do it, either login to MySacState or your Saclink email and locate the invitation to evaluate this class. There are two sections to the evaluation and in the second section there will be a couple of drop down menus asking you to identify the instructor and the class. My name appears there as Gregory Mayes, and this course is Philosophy 6.
As noted in class, if 90% of the class does the evaluation, everyone will get 3 extra points toward their total grade. Here is a decision problem to to think about, one that comes under the heading of Game Theory, which we haven't dealt with in this class. Suppose you reason: Well, everyone will get the points even if 10% of the students don't do the evaluation. Surely more than 90% of the people will do it, so I can just not do it, and still get the 3 points.
This is excellent self-interested reasoning! It is a problem discovered by the philosopher Thomas Hobbes and is now known as the Prisoner's Dilemma. The problem is that if it makes sense for you to reason in this way, then it makes sense for anyone to. Hence, everyone reasoning excellently to maximize their self-interest, results in nobody actually achieving it. Moral: Sometimes just doing the right thing is what actually ends up being best for you, too.
Read IPIL Chapter 12 and TFS 36.
Read IPIL Chapter 11. Re-read TFS 34 and read 35. Note: There will be some clicker questions on IPIL Chapter 11.
Exam grades have been posted. Grades posted reflect a 4 point curve. The grade on your test is the raw uncurved score. The solution has been posted to the schedule page as well.
Read IPIL Chapter 10 and TFS 32-34.
Test. Same format as before. Bring writing implements and calculator. No phone or computer calculators allowed, but I will have some calculators to lend out.
This question will be on the test.
Charles’ equipment isn’t what it used to be, so every Friday night, just before his girlfriend Bernice comes over for a sumptuous dinner prepared by Charles, he tries to remember to take his Viagra. Unfortunately, his mind isn't what it used to be either, and 50% of the time Charles forgets. Also, 50% of the time he can’t remember whether he has taken the Viagra or not. When he has taken it, and remembers he has taken it, he is capable of performing 75% of the time. When he hasn’t taken it and remembers that he hasn’t taken it, he is capable 25% of the time. On the other hand, when he hasn’t taken it, but doesn’t remember that he hasn’t taken it, he still is capable about 60% of the time. But when he has taken it, and doesn’t remember that he has taken it, he is capable only about 30% of the time. (Note: While there is a material difference between not remembering whether X, and falsely remembering that X, in this problem treat these as the same.)
Question 1: Bernice came over for dinner tonight and Charles was capable! What is the probability that Charles took his Viagra?
Charles is asked to rate the value of a Friday night with Bernice by determining how much money he would be willing to pay to prevent if from being cancelled on any given night. Charles finds this way of evaluating his evenings very distasteful, but he nevertheless answers as follows:
Using these answers, what is the expected value for Charles of the act of spending a night with Bernice? (Note: you may think of the consequences as Capable and ~Capable. But remember there are 4 ways in which each of these can occur, so compute the probabilities accordingly. Alternatively, you may think of this as 8 distinct consequences that are conjunctions of three events. e.g. C1 would be: V & R & C.)
Charles sometimes gets leg cramps and diarrhea the day after Bernice visits and his doctor is concerned that it is due to the Viagra. So he tells Charles to discontinue using it, which he does, and the symptoms do in fact disappear. But Charles capability frequency on Friday evenings drops to .25.
Question 3: Using the same scale, assuming Charles is satisfied with this result, what is the least amount that he is willing to pay to avoid these medical symptoms?
An expanded version of the notes on expected value has been posted. The derivation of Bayes' Rule for two mutually exclusive hypotheses is at the beginning. You will need to be able to reproduce this from memory. You will also need to write down the formula for the expected value of an act A with two mutually exclusive consequences C1 and C2. It is:
Exp(A) = [Pr(C1) U(C1)] + [Pr(C2) U(C2)]
The test itself will have 1 other question that is identical to a problem in the notes, so be sure you able to work all of them.
Also, by Sunday night I will post a problem here that will be on the test. It is ok for you to collaborate on working on this one outside of class, but not during the test. Don't wait until the day of the test to solve it, you'll be a sad camper. This test will focus on expected value calculations, but, as before, there will be a few short answer questions on concepts from TFS Chapters 20-31.
Re-read Allais Paradox in Kahneman (Ch 29), and IPIL (Chapter 9). Be sure you have worked through all solved problems in IPIL Chapter 9. The Wikipedia entry may help you as well. Read Chapter 31 Kahneman.
Chapter 29 and 30 TFS. And work the following problems. (Slides containing solutions to all expected value problems we've worked to date are on the schedule page.)
1. You are invited to play the following game. I flip a coin. If it lands heads, the game is over and I will pay you a dollar. If it lands tails you get nothing, but I will flip again. This time if it lands heads the game is over and I will pay you 2 dollars. If it lands tails again, I must flip again. This time the payment for heads will be 4 dollars. The game must continue as long as tails keeps coming up. The game must end as soon as heads comes up, and the payment must be exactly double the preceding amount promised for heads. The game continues until the coin lands on heads. What is the expected value of this game for you?
2. You are in a hurry to see a client. She is impatient, and if you are not there in time, you will not get a job that is worth 500 dollars more than the labor you will put into it. However, to get there in time you will need to exceed the speed limit and the cost of a speeding ticket in this area is 275 dollars. If the probability that you will get a ticket when speeding in this area is 30%, what is the lowest probability of losing the job that will make it worth it to speed? (Assume that there are no other costs to consider in this case, such as risk of accident.) Assume that getting a ticket will detain you long enough to be too late to get the job, and that you are certain to get the job if you arrive on time.
3. You are on the show Let's Make a Deal! There are three different doors and three different prizes: $1,000, $5,000, and $10,000. You choose a door and before it is opened Monty Hall opens another one to reveal 5,000 dollars. He then offers to let you switch. What is the expected value of switching?
4. The best data to date suggest that the flu shot is about 60% effective in preventing the flu in people under 65. Also, in any given year, the likelihood of any individual getting the flu is around 10%. What is the probability of getting the flu, given that you have been vaccinated? What is the probability of not getting the flu, given that you have been vaccinated? (This is a probability problem,not an expected value problem. Do a tree.)
5. Let's suppose that a flu shot costs you 15 dollars as well as another 15 dollars worth of inconvenience and discomfort. Let's also suppose that, for you, getting the flu has a negative utility of about 300 dollars. (In other words if you were certainly going to get the flu, you'd be willing to pay 300 dollars to stop it.) Using the calculations from 4, figure out which act has more expected value for you, getting vaccinated or not getting vaccinated.
Chapter 27 and 28 TFS.
Our next test is November 13th. (And there will be no class on the 15th.)
Work these problems, and be sure you have done 3 and 4 from 10/30, as we'll start with those.
1. You are working on an exam and it is getting late. There are two remaining problems and you only have time for one. Problem A is worth 3 pts, Problem B is worth 5 pts. This suggests that A is supposed to be easier than B, but it’s not certain. Also, in this test you actually lose half the value of the question if you get it wrong. Suppose the probability of your solving A is .8 and the probability of solving B is .3. Calculate the expected value of each problem.
2. An elderly lady has stepped out in front of the light rail. She will certainly die if you do not help her, but you can not help her without risking being killed yourself. People of her age and condition have an average of 10 QALY’s remaining. People of your age and condition have an average of 50 QALY’s remaining. If you save her, you will both live without injury. If you fail to save her, you will both die. Using the above figures and taking only your and her QALYs into account, what is the lowest probability of success that will make the expected value of trying to save her worth the risk? ( QALY means “quality adjusted life year.” It is a way of quantifying a person's quality of life. A QUALY is just the amount of utility in an average year of human life. So, for example, an insurance company may refuse to pay for an operation because even though people can be expected to live 5 extra years on average, they only get 2 QUALY's, meaning the amount of utility that one would normally get from living 2 years.).
3. There is 1,000 dollars on the table. You and Ralph are to split it with one of you getting 800 and the other getting 200. You are the one who gets to decide. The problem is that if Ralph is dissatisfied he can choose to kill the whole deal, in which case neither of you will get anything. Suppose that Ralph certainly would not kill the deal if you gave him the 800. Ralph might very well kill the deal if he only gets 200 though. What is the minimum probability of this occurring that would make it rational for you to give him the 800? (In this case you and Ralph are never losing any money. You are only gaining 800, 200, or nothing.)
4. In the U.S., it is a fundamental principle of jurisprudence that it is worse to convict the innocent than to let the guilty go free. But how much worse is it? Let's suppose that it is 10 times worse to punish an innocent person than to let a guilty person go free? What is the lowest probability of guilt for which it would be acceptable to return a verdict of guilty? (Hint: The choice of units is arbitrary. If you assign -1 to the outcome of letting a guilty person go free, then assign -10 to the outcome of convicting the innocent. )
Read chapter 9 IPIL and chapters 25 and 26 TFS. Work the problems below, they will be on the quiz.
1. You are at your favorite restaurant and trying to decide whether to order your old standby (pizza) or something different (lasagna). The pizza costs 10 dollars and you always get total satisfaction from pizza, which is to say 10 dollars of value. (This makes the expected value of the purchase 0.) The lasagna also costs 10 dollars. If you try the lasagna and are satisfied, you will get bonus pleasure of having tried something new worth 5 dollars, for a total utility of 15 dollars. But if you get the lasagna and you are anything less than satisfied, then you will suffer the extra pain of regret for not having had your old standby so that you would only get 2 dollars worth of value from the lasagna. Question: What is the least probability of satisfaction that would be required to make it worth it to you to try the lasagna?
2. You’ve decided to rent a classic black and white movie on Amazon. You have narrowed it down to two choices. Citizen Kane and The Maltese Falcon, neither of which you have seen. CK costs 5 dollars and the personalized rating system says that there is an 80% chance that you will like it. MF costs 3 dollars and the rating system says that there is a 60% chance that you will like it. Assuming that the rating system is accurate, and liking the movie means that it was a fair price and disliking it means you got no value, what is the expected value in dollars of each of these purchases? (CK, MF)
3. Your dog just got run over and it is going to cost 2,000 dollars to fix him up. Prior to the surgery the dog's life expectancy was 5 more years. If you opt for the surgery it will still be five years, but the quality of life will be 80% of normal. If you don't do the surgery, you will pay 100 dollars to have your dog euthanized and you will feel 400 dollars worth of remorse and guilt. What does the dollar value of the rest of the dog's life have to be in order to make the surgery worth the money?
4. You mow the lawn for the old lady who lives next door. Theoretically she pays you 50 dollars each time you do it, which in your view is 10 dollars more than the fair price. But in reality she completely forgets to pay you about 25% of the time and you just never have the heart to tell her when she does. Over the long run are you getting overpaid or underpaid, and by how much?
Read TFS 23 and 24 and work the following problems, which will be on the quiz.
1. Suppose you want to buy a 1 million dollar life insurance policy for a flat rate to cover the next 20 years of your life. What would be a fair price if the risk of your dying at anytime during this period is .01? Remember, the expected value of a fair price is 0. (The actual number of years of the policy doesn't figure into this calculation.)
2. Suppose you are invited to play Rock, Paper Scissors for money. The deal is this. You pay 1 dollar to play. If you tie you get 50 cents back. If you win, you get 3 dollars back. If you lose you get nothing. What is the expected value of this game?
3. You can play this game for one dollar: Roll a die. If an odd number comes up, you are finished and you have lost your dollar. If an even number comes up you get the value of that number in dollars. What is the expected value of this game?
4. You are planning to study for your test tomorrow but your friends want you to come over and party. You figure there is a 70% chance you will pass even if you don’t study and there is a 90% chance that you will pass if you do study. Suppose partying is worth 5 utiles. Studying is worth 1 utile. (Yes, you enjoy studying somewhat.) Passing the test is worth 5 utiles and failing it is -5 utiles.
What is the expected utility of partying ?
What is the expected utility of studying?
5. You just bought a new laptop for 1500 dollars and you are trying to decide whether to buy the insurance, which costs 150 dollars and covers you for two years. The insurance covers any breakage. Let’s assume there is a 10% chance that your computer will break during this time, and the average cost of repair is 400 dollars. Is the expected value of buying the policy higher or lower than the expected value of not buying the policy? By how much?
Work solved problems in IPIL Chapter 8 and read Chapters 21 and 22 in TFS.
Read Chapter 8 IPIL and Chapter 21 TFS.
Read TFS Chapter 19 and 20. Solve the following conditional probability problems using Bayes' rule, then use a tree to check your results. (Be sure to do them, because they will be part of the quiz.)
1. It is Monday morning and you are lying in bed trying to decide whether to get up.Your roommate always leaves for school before you wake up, and you don’t want to get out of bed this early unless the coffee has been made. Your roommate makes a pot of coffee (and leaves enough for you) about 25% of the time. (Assume that when she makes it, there is always enough left for you. Nobody else makes coffee.)
80% of the time when she makes coffee you can smell it from your bed. But 20% of the time you can’t. 70% of the time when she doesn’t make coffee, you don’t smell it. But 30% of the time you have an olfactory hallucination and smell it when it’s not there.
What’s the probability that the coffee has not been made, given that you smell it?
2. Frank arranged to study with his friend Ray for a logic exam. Frank's not a great student, but studying with Ray boosts his chance of passing from 50% to 90%. Unfortunately, Ray is not reliable, and will just flake and not even show up to study about 25% of the time. It turns out Frank passed the test. What's the probability that he studied with Ray?
3. Your neighbor Fred has just been arrested because his fingerprints match those found on a weapon that was used in a murder in another part of town. Fred claims to have been alone at home the night of the murder, but there is no one who can vouch for his whereabouts. Nothing besides the fingerprints tie Fred to the victim, the weapon or the scene of the crime.
Fred’s fingerprints were the only match in a database of 10,000 people all deemed equally likely to have been involved in the crime. With fingerprints, the probability of a false positive is .01. The probability of a false negative is .07.
What is the probability that those are Fred's fingerprints on the gun?
Note: "False positive" in this case means that the test says that these are Fred's prints, but they actually aren't. "False negative" in this case means that the test says they are not Fred's prints, but they actually are. In statistics, a false positive is called a Type 1 error and a false negative is called a Type 2 error.
4. (Note: this is the example we did in class, but the question is different.) You have just tested positive for a rare disease called Uh-oh. By rare, we mean that it occurs in 1/10,000 people. In other words, for any randomly selected individual, the likelihood that he or she will have Uh-oh is .0001 The test is 99% effective. This means: 99% of the people who have Uh-oh test positive for Uh-oh. 99% of the people who don’t have Uh-oh, test negative for Uh-oh.
You tested positive for Uh-oh. Your doctor said that the probability is not high that you have it given just one test, so she orders it again, but again it comes back positive. Now what is the probability that you have Uh-oh?
Read TFS Chapter 17 and 18. Work solved problems in Chapter 7 IPIL.
Read TFS Chapter 15 and 16. Read Chapter 7 IPIL Bayes' Rule and work solved problems by 10/11. Work especially hard at understanding how Baye's Rule is derived, as you actually will be required to do this on the next test.
Test! All instructions below.
Our first test is on Thursday 10/4. You will need nothing but sharp #2 pencils with erasers and a calculator if you have one. I will bring a supply of calculators, but I don't have quite enough for everyone, so please bring your own if you have one. I can not let you use the calculators on your phone, tablet, or ipad for the test. In class I said that the test would partially consist of multiple choice questions on TFS, but I have decided against this.
I have posted a practice test and a solution to the schedule page. The test you do will be similar, but it will also contain a few conceptual questions relating to both IPIL and TFS. The solution only uses trees in a couple of instances, but you should use them whenever they will aid you in representing the problem.
This is important: You will not get any credit at all for answers where work is not shown clearly. Your method of deriving the answer to any problem must be transparent. By the same token, if you have the problem set up correctly, and produce the wrong answer a result of a minor mathematical or calculator error, you will still get partial credit, and sometimes even close to full credit.
For Tuesday read TFS 13 and 14. We will also work through the derivation of the formula for adding probabilities with overlap as well as the formula for total probability.
Slides for conditional probability and the rules of probability are posted to the schedule page.
Read Chapters 11 and 12 of TFS. Study the proof of the overlap rule in IPIL Chapter 6. Work the following problems, which will be on the clicker quiz Thursday. These are a little different, so give yourself plenty of time.
Urn1 Red = .8, Green = .2
Urn 2 Red = .4, Green = .6
1. Two urns are filled with red and green M&M’s in the given proportions. You flip a coin to decide which urn to draw from, then you draw two from that urn with replacement. On the first roll you get a red one. What is the probability that you will get a green one on the second roll?
2. Two urns are filled with red and green M&M’s in the given proportions. You flip a coin to decide which urn to draw from, then you draw two from that urn with replacement. On the first roll you get a red one. On the second you get a green one. What is the probability that they came from Urn 2?
3. A single urn has 9 fair coins and 1 two-headed coin. Someone reaches into the urn, randomly pulls out a coin, and begins flipping it. Question: How many heads in a row are needed before you can be 90% sure that it is the two-headed coin?
4. You are about 80% sure that your nephew Dicky just peed in the pool. Dicky will always deny his own wrongdoing, so you ask his brother Ryan, who had a clear view, but who is also a jerk. When Dicky hasn’t done anything bad, Ryan will still blame Dicky about 25% of the time. When Dicky has done something bad, he will cover up for him about 10% of the time. What is the probability that Dicky peed in the pool given that Ryan says he didn’t?
5. Manny and Gwen just bought a ticket to play cornhole at the carnival, a game in which you throw beanbags through a hole in a piece of plywood. Manny and Gwen each get three beanbags. If either Manny or Gwen gets all 3 beanbags through the cornhole, they win the stuffed barracuda Gwen is one of the best cornholers in the county with a hit rate of .9. Manny's hit rate is only .6. What is the probability that they get the barracuda?
Read Chapter 6 IPIL and Chapters 9 &10 from TFS. We will be working on conditional probability problems and the formalized expression of the axioms of probability.
Review TFS 7 and read TFS 8. Work solved problems from IPIL chapter 5 and be sure to memorize the formula for conditional probability.
Read TFS Chapter 7 and 8. Read Chapter 5 IPIL. Review lecture slides for Chapter 4, which have been uploaded to the schedule page. Be sure you can work every problem in those slides! If you can't, you absolutely need to come to see me in office hours pronto. The 1st exam has been scheduled for October 2.
Read TFS Chapter 6 and be sure you've worked through all solved problems in Chapter 4 IPIL. We will work more in class.
Work the solved problems at the end of chapter 4 and read TFS Chapter 4 and 5.
For Thursday work problems at the end of Chapter 3 (Answers are in back of book). Read Chapter 4 of IPIL and Chapter 3 of TFS.
For Tuesday read Chapter 3 of IPIL and Chapters 1 and 2 of TFS.
Hi and stuff
Hey everyone, this What's Up page is the one you will check regularly to find out about your daily assignments. Please read every bit of what follows, super carefully and do what it says to do.
First, you should have received an e-mail already telling you that we will not meet the first day of class. (This is just an odd thing due to a personal situation.) If you didn't receive the e-mail, it is probably because you aren't checking the one you have on file with the school, so you should be sure to do that.
Second, before Thursday 8/30 make sure to:
Everything else below
Before Thursday 8/30 you should have done the following:
1. Get your course materials, which consists of two texts and a clicker (see below).
2. Register your clicker online (see instructions below) and bring it with you the first day of class. We will have our first quiz, which covers the content of the syllabus.
3. Read the syllabus carefully (see link to syllabus on main page).
These are the course materials you will need to buy or rent.
You can get these all at the Hornet bookstore. It is fine to buy the Kindle editions of the texts. (Note: If you already own one of the early model e-instruction clickers that looks like this, it will work. But otherwise get the one offered at the bookstore. There are several different kinds of clickers being used on campus, so be sure to get the one made by e-instruction.)
Instructions for registering your clicker.
You will need to go online and register your clicker for this class. Register it according to the instructions on the box or those you were provided with when you purchased or rented it. You will require a credit card. Be careful to register the serial number of your clicker accurately. At some point during the registration process you will be prompted for a class key. This is a unique number associated with the class in which you are enrolling. The class key for this class is:
N72869I8363 (The character following the 9 is the capital letter I, not the number 1.)
If you do not have a box or instructions for registering your clicker, then do one of the following.
1. If you just acquired this clicker, then click here to register it. You'll need a credit card and the class key above.
2. If you are using a clicker that you have previously registered, click here and log in. Then follow the instructions given in 1 above.
3. A few important points about clickers.