Note: I just realized that in my haste to get today's test graded I actually posted an incorrect solution to the 2nd problem. A few of you may see about a 2pt rise in your grade as a result. Nobody will see a lowering of their grade. Stay tuned.
Update: The correct solution is now up. Unfortunately, I don't have the tests at home with me and won't be able to update scores until next week. However, if you recognize your solution here then you will almost certainly be getting a 2pt rise in your grade on that test (assuming you got an 8 or less). If you recognize that this is in essence your solution but that you made some kind of small mathematical error, then plan on about a 1 point rise. Sorry for the initial confusion.
Results of Test 11 are posted as well as quizzes 23 and 24. Also, 26 out of 27 currently active students have done the evals, so everyone get 5 extra points added to their total. To find out where you stand right now, add your 10 best test scores to your 20 best quiz scores. Then add your 5 evaluation points and divide the total by 200. See the grading rubric in the syllabus.
(If you got credit for writing extra credit summaries, then for each summary you got credit for, raise your lowest quiz score to a 5. E.g, if you did two summaries and your lowest 2 quiz scores are 1 and 2, then raise those both to a 5. It doesn't matter whether you do this before or after you identify your 20 highest scores. It comes out the same.)
Solution to Test 10 has been posted. Most people struggled, best to review before Thursday. Here is the scenario for Thursday's test. It shouldn't be be too hard to figure out what sort of questions I'll be asking you.
You are at a shooting gallery and you have paid 10 dollars for a maximum of 3 shots. If you hit the bull's eye with the first shot, you are done and you win 25 dollars. If you miss you can shoot again. If you hit the bull's eye with the second shot, you get 50 dollars. If you miss, you can shoot one last time. If you hit the bull’s eye on your third shot, you get 100 dollars. It is not at all easy to hit the bull’s eye, so it seems foolish to waste any of your shots for a chance to shoot at a higher value. But you’re not sure. Suppose that when you are taking a shot seriously, your ability with the rifle will increase on the next shot. In this case, the first shot you take seriously has a 10% chance of hitting the bull's eye, the second shot 20% and the third shot 30%. When you waste a shot, your ability with the rifle does not increase on the next shot. However, if you waste the first two shots, your probability of hitting the bull's eye on the 3rd will be 20% due to a spike in concentration. (Negligible increases of concentration when wasting only the first shot).
On Thursday (last day of class!) we'll have another split quiz. The first will be on the concluding chapter of TFS and the second will be on Chapter 11. Read them both carefully. We'll finish with a test similar to the last few.
Thursday will probably complete the class for most of you. You will have taken 23 quizzes and 12 tests. The syllabus promises approximately 24 quizzes and 12 tests, so we have satisfied the requirements of the syllabus. However, besides the option I've outlined (see post below) for the day of the final anyone may also show up to take another quiz and another test. The quiz will be a more or less random selection of 10 previous TFS slides. The test will be a more than ordinarily challenging probability/expected value problem, which you may have the entire period (2 hours, minus the time it takes to do the quiz) to complete.
If you are in danger of failing the class and want to take the optional final, I would strongly advise that you do not plan on taking the 13th test, since it will be very difficult to complete both. The best way to study for the final is to review all the tests we have taken to date.
Please do the course evaluations. You have received an invitation to do so in your Saclink e-mail. For those of you who have done well enough in the class that you do not need the extra points (and do not particularly care to help out your fellow classmates) I am still very interested in how you experienced this course, so please take the time to give me your honest thoughtful feedback.
Note: A fresh copy of the second problem for Test 10 are at the bottom of the schedule page, but it is toward the top of the list as 10b.
For Tuesday read TFS 38 and read Chapter 11 IPIL. We'll have another split quiz, one covering TFS 39 and the other covering Chapter 10 and 11 of IPIL. You will get the first 15 minutes of class to do the first problem of Test 10 and you'll submit that with the second problem, which I gave as a take home. A fresh copy has been uploaded to the schedule page.
Please do the course evaluations for the course right away. The last possible day to do it is the last day of next week but don't wait until then. I should be be able to let you know on Thursday how many people have done it. The is the incentive stated in the syllabus.
.. all students will receive 3 extra points if 85% of students participate in the survey, 4 points if 90% participate and 5 points if 95% participate. (These are mutually exclusive options, only one applies.)
There is no mandatory final exam for this class. However, on the day of the final exam (Thursday December 19th 12:45) you will be able to take a 13th test if you so desire. I will also have a final exam available that some people may take. To be eligible to take the final exam you must
Anyone who meets these criteria and gets a 75% or better on the final will get a C in the course. (You can not do better than this.) You will have an hour to do the final. It will be a cumulative test. It's important to understand that this test is an opportunity for people to show that they understand the material despite experiencing problems early on. It will be a poor use of your time to take the final if you do not understand the material.
Finally, please pay attention to the manner in which your grade for this class is calculated. Simply add your best 20 quizzes and your best 10 tests and divide by 200. If you have submitted colloquium summaries, then follow the instructions on the syllabus. If extra credit occurs as a result of peopple doing course evaluations, you will simply add those points to your total (before dividing by 200.)
Read TFS 37 and review Chapter 10 of IPIL. Quiz, then test. Check back here a little later for sample test problems.
1. You flip two coins blindfolded, one after the other. You ask your friend Og if at least one of them landed heads. Og say yes and Og not lie. You may now place a bet on how the other coin has landed. If you win, you get 100 dollars. If you lose, you get nothing (i.e., in both cases your original 50 is a loss.) What side should you bet on and what is the expected value of this bet?
2. You have 1,000 dollars and Og has diddly squat. Assume that the utility of money follows the square root function. (This makes the utility of 1 dollar = 1 utile; the utility of 100 dollars = 10 utiles, etc.)
3. There are three cards face down on the table. Card A is worth 5 dollars. B is worth 20 dollars. C is worth 50 dollars. Assume the square root function for utility.
The test on Tuesday was converted to a take-home test and may be found at the bottom of the schedule page as Test 9. As before, the standard on a take-home test is that it must be perfectly legible, explicit and organized with no math mistakes of any kind to get credit. It is due at the (correction) beginning of the period. You may turn it in if you were absent on Tuesday and you may redo it if you turned it in already but believe one or more of your answers to be incorrect.
For Tuesday read TFS 36 and Chapter 10 of IPIL. Also, review chapter 29 of TFS on Allais paradox. I will post chapter 9 notes covering the same (which we haven't gotten too in class yet.) As we are a little behind on quiz opportunities, I am going to split the quiz on Tuesday into two. They will cover all of the above.
Happy Thanksgiving and Hanukkah!
Quiz over TFS 35 and Chapter 9 IPIL. Most people had some type of difficulty with test 8. Study the posted solution. We will finish the period with a very similar test. (Remember, the more tests the better.)
Here are some more problems to work as well. (Work them! They may be on the quiz.)
1. There are 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. But Ralph might very well kill the deal if he only gets 200 . What is the minimum probability of this occurring that would make it rational for you to give him the 800? (Remember, killing the deal doesn't mean you've lost any money. You don't have any yet.)
2. 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 (i.e., that the defendant actually committed the crime) 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. )
3. Beef is playing a game. He is going to roll a die and if it comes up 6 he's going to steal 100 dollars from Ted (for any other number he leaves Ted alone). But Beef tells Ted that if Ted pays money in advance, they'll play a different game instead. In this game Beef rolls the die and if it comes up 6 Beef has to roll again (otherwise leaving Ted alone), with the original conditions stated applying to the second roll. If Ted is an econ, what is the highest amount of money he'll be willing to pay to Beef to play the second game rather than the first?
Read TFS 34. We'll have a brief quiz over it and some more problems which I'll post by Wednesday morning. Then we'll have a test on expected value problems. Slides with solutions to problems covered in class Tuesday will be posted as well.
1. Do last two flu shot problems from previous assignment below. Then review solutions.
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 the job. The job is an easy one, worth 500 dollars more to you than the labor you will put into it. If you drive the speed limit, there is a chance that you will not get there on time. If you speed, you will get there on time, but only if you don’t get pulled over for speeding. If you get pulled over, you will get a ticket for 275 dollars and then you definitely will not make it in time to get the job. If the probability that you will get a ticket when speeding in this area is 30%, what is the lowest probability of not getting the job that will make it worth it to speed?
3. An elderly lady has stepped out in front of the light rail. She will certainly be hit and 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?
Note: 'QALY' means "quality adjusted life year" and it is used by insurers to calculate the value of medical intervention. For example, in the dog surgery problem (2) below you were told that the dog's quality of life would be 20% of normal after surgery. This means that each year of life would be .8 QALY's. Since the dog was projected to live 5 more years, this means he was projected to live for .8(5= 4 QALY's.
Read TFS 31-33 and work the following problems. Chapter 8 slides will be updated with answers to problems from 11.14 and the solution to Thursday's test has been uploaded to the schedule page.
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 which you regard as a fair price. 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. 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?
3. 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?
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%.
a. What is the probability of getting the flu, given that you have been vaccinated?
b. What is the probability of not getting the flu, given that you have been vaccinated?
5. Suppose the total cost of a flu shot to you (including pain and inconvenience) is 20 dollars.
Suppose also 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, but no more, to stop it.)
Using the calculations from the previous problem, figure out which act has more expected value for you, getting vaccinated or not getting vaccinated.
Thursday we will continue to work expected value problems and then take a test. Do these ones in preparation. Chapter 8 slides were updated 11/13.
1. You have a bike worth 1,000 dollars. You are trying to decide what sort of lock to buy for it. Lock A costs 10 dollars. Lock B costs 100 dollars. If the probability of your bike being stolen with lock B is .01. What is the highest probability of theft with lock A for which the purchase of Lock A would not be irrational? (Think of the purchase of the lock as a net loss. The lock’s only value to you is as something that will prevent the theft of your bike.)
2. 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. Your risk of dying at anytime during this period is .01. The policy costs 20,000 dollars. What must your peace of mind be worth in order for this to be a fair price? (Note: For this example, think of peace of mind as something you get all at once when you purchase the policy, rather than as something distributed through the 20 year period.)
3. 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. Assume there is a 10% chance that your computer will break during this period.
The average cost of a 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?
4. Mel is in reasonably good shape for an 85 year old, but he has no savings and his wife Mildred will not get his pension when he dies. For a man of Mel's condition and age, there is a 10% chance he will die in any given year. For a little peace of mind, Mel would like to buy a 200,000 dollar policy to cover the next 5 years of his life. If you were willing to sell Mel a policy at a fair price to cover this period, what would you have to charge him? Note: You'll need to think a bit about how to represent the probability that Mel will die during one of these 5 years. For example, the probability that he dies in year 2 must reflect the fact that he did not die in year 1.
5. Manny and Gwen are playing cornhole again at the county fair. Manny has a hit rate of .6 and Gwen has a hit rate of .9. 1 ticket costs a dollar and gives you three beanbags to toss. If you get 1 bag in the hole you get 50 cents. If you get 2 bags in the hole you get $1.50 and if you get 3 bags in the hole you get $3. What is the expected value of Manny's game and what is the expected value of Gwen's game?
Finish Chapter 8 if you have not, pay particular attention to the St. Petersburg Game. Read TFS 28-30. We will have a quiz covering the above and problems like the following. Notes containing problems we worked on 11/7 will be posted to the schedule shortly.
1. 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?
2. 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?
3. 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. How does the expected utility of partying compare to that of studying?
4. There are 2 coins in a bag. One is a fair coin. The other has a 90% bias toward heads. You have a choice between two coin flipping games in which you will flip some coin twice. Both of these games cost 3 dollars to play. The payoff for each of these games is as follows.
TT = $6; HH = $4; TH = $1; HT = $1
Game 1: You choose a coin randomly and flip it twice in a row.
Game 2: You choose a coin randomly and flip it. You replace the coin in the bag. You choose a coin randomly again and flip it.
Which game has a higher expected value?
Work the solved Chapter 8 problems from IPIL and read chapters 26 and 27 of TFS. We will not have a test on Thursday, but we will have a quiz over TFS and elementary expected value problems like these:
1. We will flip a coin. If it comes up heads, I will give you 15 dollars. If it is tails you will give me 10.
What is the expected value in dollars of this game to you?
2. You owe me 10 dollars. Before you pay, I offer you this deal. We will flip a coin. If it is heads, you owe me nothing. If it is tails you owe me 15. What is the expected value of this offer to you? How does it compare to the expected value of just paying what you owe?
3. You bought a piece of artwork while touring South America for 5,000 dollars and are sending it home by mail. If the price reflects its value, and the probability of it being lost or destroyed is 5%, what is the fair price for insurance?
Please read Chapter 8 of IPIL and 23-25 of TFS. We'll have a quiz on the latter on Tuesday, review Chapter 8 and work some elementary expected value problems. Update versions of Chapter 7 notes with solved problems we reviewed on 10.31 will be posted this weekend.
We will have a test on the application of Bayes' Rule to slightly more complicated/interesting examples. Here are some for you to work on in preparation. We will review those we have time for prior to the test. I will post a revised set of Chapter 7 notes including a discussion of the Monty Hall problem shortly.
1. You are on the Monty Hall Show and Monty has allowed you to choose between door A, B and C. Behind 2 of the doors is a goat, behind the other is a new car. You have chosen door A. Monty then spins a wheel to (which we will assume is an effective randomizer) determine what door to open. The wheel lands on door B and Monty opens it, revealing a goat. He then asks you if you would like to switch doors. Use Bayes' rule explicitly to figure out the probability that the car is behind door C. (Note: We must assume here that Monty will open whatever door the randomizer lands on, which means that he might have opened the door with the car.)
2. The same situation as above, but instead of using his randomizer, Monty Hall flips a coin to decide which of the remaining two doors he will open. The coin lands on B and he opens it to reveal a goat. Use Bayes' rule explicitly to figure out the probability that the car is behind door C.
3. Hank is a master chicken sexer with a rating of 99. This means that Hank is 99% reliable in determining the sex of baby chicks. (You can read about chicken sexing here, but you don't need to in order to do the problem.) Hank is a teacher and has a large group of apprentice chicken sexers all of which have established an entry level rate of .65.
Suppose Hank is testing his apprentices. He randomly selects a chick from a box that is 50% roosters and 50% hens. He looks at the chick and sexes it as a rooster. He then puts it into a box for each apprentice to sex independently.
Suppose that the first apprentice independently sexes the chick as a hen, and that each succeeding apprentice also independently sexes it as a hen.
At what point (if ever) does it become more likely that the apprentices are right than that Hank is right?
4. Fred and Mary are journeyman level chicken sexers. Fred is .7 reliable when the chicken is a rooster and .8 reliable when the chicken is a hen. Mary is .6 reliable when the chicken is a rooster and .9 reliable when the chicken is a hen. Fred picks up a chicken and sexes it as a rooster. Mary independently sexes it as a hen. What is the probability that it is a hen?
5. Jane is going to watch a movie on Netflix. She's narrowed it down to 3 choices: Gladiator, The Hangover and Ratatouille. She can't make up her mind, so she writes their names on the back of 3 well shuffled cards and will choose one. Afterwards she'll invite her friend Barb to watch the movie with her. She knows Barb's tastes well. The respective probabilities that she will come and watch the movies are:
I gave you Test 5 on Thursday as a partial take-home test. For those of you who weren't there, I have uploaded a pdf version of thist test to the bottom of the schedule page.
Here are the instructions: Work the 2nd problem in it's entirety before coming to class. It is ok to collaborate. Because it is a take-home and you have ample time to make it neat, it must be done exactly correctly and be absolutely legible. If it is even the slightest bit messy or disorganized you will get zero credit for this problem. (If you are wondering just how serious I am about this, imagine that you will be beheaded if it does not look good enough to be an illustration of how to work the problem for a textbook written before there were printing presses.) You must make both numerical calculations explicitly and show all of your work, including the tree representation(s). Leave the first problem, the derivation of Bayes' rule, blank. You will be given about 5 minutes at the beginning of class to do this problem.
Look at the Chapter 7 slides to see exactly how to do the derivation, including the justifications. There is one slide on which the entire derivation is presented. You can do it differently, but be sure each step is justified.
For Tuesday, read chapter 21 and 22 of TFS and review Chapter 20. We will have a quiz over these chapters and review the generalized version of Bayes' Rule and show how it can be used to solve the Monty Hall problem. If you are not familiar with this problem, you should read about it on Wikipedia.
Read Chapter 20 TFS and review derivation of Bayes' Rule, now posted in Chapter 7 notes. For the test you will need to derive Bayes' rule and work problems similar to those from 10.17 and others I've posted at the end of the Chapter 7 notes. We'll work as many of those as we have time for on Thursday.
Read Chapters 18 and 19 of TFS and Chapter 7 of IPIL. Work solved problems in IPIL. Quiz covers both. Also watch this TED video. Also be sure you have worked all the problems from 10.15 and work these problems as well. Quiz will cover all of the above. Solution to test 4 is posted to bottom of schedule page.
1. 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.
2. 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.
What is the probability that you have Uh-oh, given that you have tested positive? Pr(U/P)
3. You have tested positive for the rare disease called Uh-oh described above. 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?
On Thursday we will have a test in which you will be asked to prove the rule for overlap from the truth table definition of disjunction and the formula for total probability. The test will also include a probability problem. Here are some additional solve before then. We will work on as many as we have time for.
1. 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: Beginning with the first flip, how many heads in a row would be needed before you can be 90% sure that it is the two-headed coin?
2. You are at a very large Pilates class in which only 5% of the students are male . You look at someone across the room who you feel sure is male. How reliable must your sex detection abilities be in order for it to be 95% probable that the person is male?
3. 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 coffee?
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 little jerk. When Dicky hasn’t done anything bad, Ryan will still blame Dicky about 25% of the time. When Dicky really has done something bad, Ryan will actually 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? (For simplicity assume that Ryan definitely knows whether Dicky peed in the pool or not.)
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 cornhole players in the county with a hit rate of .9. Manny's hit rate is only .6. Manny and Gwen came home with the barracuda! What is the probability that Gwen did not get 3 bags through the hole?)
Be sure you have carefully worked through the posted notes on Chapter 6. We will not have a quiz or test, but there will be a quite dense lecture on Chapter 6. Notes to chapter 6 now contain the overlapping probability problems we worked in class. On Thursday we will have a test, one of the problems will be to prove the addition rule for overlapping probabilities. This is fully worked out in the notes, and we will review it on Tuesday.
Review chapter 17 of TFS. There will be no test Thursday, but there will be a clicker quiz on 17 and the probability problems below. Work them out before class. We will continue to review chapter 6 of IPIL. Please refer to the posted notes on this chapter to understand what you will be held accountable for. (I will be putting up a slightly revised copy of these this morning.)
1. In the helping experiment described in chapter 16 of TFS, roughly 27% of the people help. Suppose that 'Caring' is defined technically and can be measured. Suppose further that of people that help, 80% are Caring and that of people who do not help, 50% are caring. Angie is a Caring person who participated in the experiment. What is the probability that Angie helped?
2. Two urns contains M&M's in the following proportion:
Urn A: 30% yellow, 60% red, 10% green.
Urn B: 10% yellow, 30% red, 60% green
You draw two M&M's randomly from Urn A with replacement. You also draw two M&M's randomly from Urn B with replacement. What is the probability that you will draw a red and a green from Urn A or from Urn B?
3. Manny and Gwen are shooting free throws in basketball. Manny sinks baskets at a rate of .7 and Gwen sinks them at a rate of .5. If Manny and Gwen both take two shots, what is the probability that Manny sinks both baskets or Gwen sinks both baskets?
Read chapter 15-17 of TFS and chapter 6 of IPIL. Quiz on Tuesday over TFS chapters. Chapter 6 of IPIL is short but a little tough going in places, so I will post complete notes on Chapter 6 sometime this weekend. I'll also update the notes to Chapter 5.
Important: I can't make my normal office hours on Thursday 10.3, but I will be there from 10- 11:30.
Review chapter 13 and read chapter 14 of TFS. Be sure you have worked through all problems in Chapter 5 of IPIL, and work the problems below as well. The Chapter 5 from 10/1 will be posted by 10/1 at midnight. We will quiz on TFS and the problems below then take a test on CP problems.
1. You are in a particularly nasty part of town where 20% of the male pedestrians will rob you and 10% of the females ones will. You eye a person coming down the sidewalk. You are 70% sure it is a female (hence, 30% that it is a male.) Shit! You just got robbed by that person! What is the probability that it was a female?
2. Two urns are filled with red and green M&M’s in the above proportions. You flip a coin to decide which urn to draw from, then you draw two from that urn with replacement. On the first draw you get a red one. What is the probability that you will get a green one on the second draw?
3. Two urns are filled with red and green M&M’s in the above proportions. You flip a coin to decide which urn to draw from, then you draw two from that urn with replacement. On the first draw you get a red one. On the second you get a green one. What is the probability that they came from Urn 2?
Chapter 4 slides on the schedule have been updated to cover problems we did on Thursday and a few others we didn't get to. Be sure you review those.
Now that we are starting to test on quantitative aspects of probability, it's important to understand that we remain accountable for everything we have done in the past. Tests will normally cover what we have been working on recently, but will sometimes cover things we have learned in the past. This will not normally pose a problem, as the new material usually presupposes an understanding of the old. But now always. Make a habit of reviewing problems on the posted slides, especially ones we don't cover in class as they are always fair game on subsequent quizzes and tests.
For Tuesday we'll quiz on chapters 12 and 13 from TFS and review Chapter 5 of IPIL on conditional probability. Please be sure you've worked through all the worked problems in Chapter 5.
Please review chapters 9-11 of TFS and read Chapter 5 of IPIL. We will quiz on TFS, IPIL and questions 3 and 4 from Tuesday (posted below). The solution to today's test has been uploaded to the bottom of the schedule page.
Read chapters 9-11 of TFS and work the following problems in preparation for test 3 on 9/24. We will review these problems and others like them before taking the test at the end of the period.
Chapter 4 notes will be posted on the schedule shortly.
I have decided to discontinue routinely putting up the quiz results on the schedule page. Test solutions will always be posted. If you have questions about the results of a particular quiz, e-mail me and I will help you out.
1. A bag is filled with 90% fair coins and 10% unfair coins. The unfair coins have a 75% bias for tails. You reach into the bag randomly, extract a coin and flip it twice in a row. What is the probability that you will get two heads?
2. Same bag of coins. You reach into the bag randomly, extract a coin and flip it. You then replace the coin, shake the bag well, and repeat the procedure. What is the probability that you will get two heads?
3. Sam and Bernice are playing Cornhole at the county fair, a game in which one attempts to throw beanbags through a hole cut in a piece of plywood. Sam has a hit rate of .5 and Bernice has a hit rate of .75. 1 ticket gets you three tosses. If you get 2 out of 3 bean bags in the whole you get the stuffed barracuda. If Sam and Bernice flip a coin to decide who gets to throw, what is the probability that they win the barracuda?
4. Sam has signed up to take statistics. There is a 30% chance he will get Professor Urna and a 70% chance he will get Professor Burns. 90% of students who take Urna's class pass the class, but only 20% of those who do, pass the AP test afterwards. Only 50% of students who take Burns' class pass it, but 90% of those who do, pass the AP test afterwards. What is the probability that Sam will pass the AP test? (Assume that all and only people who pass the class take the AP test.)
Read chapter 8 of TFS and finish Chapter 4 of IPIL if you have not already. We will do a clicker quiz covering both chapters and then take a written test at the end of the period. Although the calculations for this test will be elementary, you should start bringing a calculator to class from here on out. Please remember that for testing purposes it can't be a calculator on a device (like your phone, laptop or tablet) that connects to the internet. I will have spares to loan, but not enough for everyone.
I've uploaded the slides for IPIL Chapter 3 to the schedule page. We didn't quite get to all of the slides on this chapter nor all the questions so you should look at these and make sure you can answer them, I'll run them as part of Tuesday's quiz. They are all just like answered problems in the book.
For Tuesday, read Chapters 6-7 of TFS and Chapter 4 of IPIL and work through the problems in the latter.
Test 1 results will be posted soon.
For Thursday read TFS Chapter 5 and finish working through Chapter 3 of IPIL if you have not. We will have a test on Thursday, but we will actually use clickers for this one and it will have the form of a cooperative quiz. Next week we will be into Chapter 4 of IPIL where we will actually start doing elementary probability calculations.
Update 1: Grades for Quiz 1 have been uploaded to Blackboard. A couple of you pointed out at the end of the period that for one of the questions I incorrectly identified the correct answer with the result that 90% of you got it wrong. I fixed this. Also, some of you will note that you have slightly over 5 points on the quiz. The syllabus says that all quizzes are worth 5 points, but I do not have a set number of questions that I ask and the software only allows me to assign point values to individual questions, not the entire quiz. Hence, I calculate and slightly round off the point value afterwards. The total possible will always be very close to 5, and never less.
Update 2: If you want to review the quiz questions, they are attached to the bottom of the schedule page as .pdf. In the future, if they are not there the day after the quiz, feel free to send me a reminder. I will appreciate it.
Update 3: In case you missed it, here is the link and the code for the 15 dollar rebate on your clicker.
Ok, it looks like everyone has been able to get both books and the clickers, so we are ready to go. Some of you have still not registered your clickers as instructed below, so be sure to do that soon. Please do not do it right before class as this can cause technical difficulties that may result in your quiz grade not being recorded.
This week we covered the first two chapters of Introduction to Probability and Inductive Logic (henceforth: IPIL) as well as the first two chapters of Thinking, Fast and Slow (henceforth TFS). I will put the slides from Chapters 1 and 2 of IPIL on the Schedule page soon.
On Tuesday we will have our first quiz, which covers the material from last week as well as the reading for Tuesday. (Quizzes will normally occur over reading material before we have discussed it in class, tests will not.)
The reading for Tuesday is Chapter 3 of IPIL and Chapters 3 and 4 of TFS.
Hi everybody, this What's Up page is where you will come to find out what's up for the next class period. Check it every day.
Here's what you you need to do to get started in this class.
1. You'll need these three things by Tuesday. (If you can't get them after class, be sure you get them before class.)
All these are available at the Hornet bookstore. Be sure that the clicker you buy is made by Turning Technlogies. Nothing else will work. You can order the books online, but I do not recommend doing so at this point in time, as you will not be excused from any reading you are unable to do because your book hasn't arrived in the mail.
2. Register your clicker immediately. You do this as follows.