EXAM 3, Practice PHILOS 111 Knachel Name________________________ Show how the following passage exemplifies the general form of analogical arguments, by identifying the a’s, P’s, c and Q. (4 pts.) 1. You’ve never had swordfish? Oh, I think you’ll like it. You like salmon and tuna, right? Swordfish is similar to those: it’s got a sturdy flesh; it’s oily and flavorful; and it can be grilled to great effect. Consider the following inductive argument. Say whether each new premise weakens or strengthens it—or has neither effect. Indicate which of the six criteria for the appraisal of inductive arguments justifies that judgment. (2 pts. each) I’ve always bought General Motors vehicles, and they’ve always been very reliable. I fully expect the GM car I just bought also to be very reliable. 2. My past GM purchases have included both cars and trucks, and I’ve had many of the GM brands: Saturns, Buicks, Oldmobiles, Chevrolets, and Pontiacs. 3. I’ve owned a whopping seventeen GM vehicles. 4. I’ve been a Buick man all my life, but this time I’m going with a Saturn. 5. In fact, all of my other GM cars never broke down or needed any repairs, and they all ended up with over 2,000,000 miles on the odometer. 6. I’ve always bought Chevy Cavaliers, and this time will be no different. Here is a refutation by analogy. Write down the argument or claim that’s being refuted, and the analogous argument or claim that does the refuting. (2 pts.) 7. The honorable senator from Wisconsin claims that if we pass his bill it’ll take the money out of politics. What’s next—a bill that takes the hydrogen out of water?In the following sentences, which sense of the word ‘cause’ is being used? Is it cause in the sense of necessary condition, sufficient condition, or neither—a mere tendency to produce a certain effect. (2 pts. each) 8. Eating lots of highly processed, sugary food causes diabetes. 9. Swimming in molten lava causes skin irritation. Respond to the following as indicated. 10. Consider the following scenario: Albert, Betty, Connie, Darryl, and Ernie went to a party at Francine's house. There was a spread of food for snacking on, which included taco dip, pita chips and hummus, pasta salad, Swedish meatballs, and cake. Later on, Albert, Darryl and Francine all got violently sick, and were diagnosed with food poisoning. Here's what they all ate at the party: Albert – taco dip, pita chips and hummus, Swedish meatballs, cake Betty – taco dip, pita chips and hummus, cake Connie – cake Darryl – everything Ernie – taco dip and cake Francine – pita chips and hummus, pasta salad, Swedish meatballs a. Using only the Method of Agreement, how far can we narrow down our choices in the search for the food that caused the sickness? (2 pts.) b. Using only the Method of Difference, how far can we narrow down our choices in the search for the food that caused the sickness? (2 pts.) c. Using the Joint Method of Agreement and Difference, how far can we narrow down our choices in the search for the food that caused the sickness? (1 pt.) 11. The usual symptoms of regular bacterial pneumonia are rapid onset of sickness, high fever, and unusually rapid breathing. If, in addition to these symptoms, the patient complains of sore throat and headache, normal pneumonia bacteria can no longer be considered the cause; the Method of Residues demands an alternative cause, which turns out to be a special bacterium: Mycoplasma. What’s the residue in this example? (2 pts.)12. We all know that too much TV can be bad for kids. Name a quantity that varies directly with the number of hours per day of television watched; then name a quantity that varies inversely with hours per day of TV. (4 pts.) Directly:__________________ Inversely:___________________ Work the following problems involving probability. Don’t carry the calculations all the way through; it’s enough to indicate that, in order to get the answer, one must multiply some numbers together, without actually carrying out the multiplication. 13. An urn contains 11 black balls, 4 white balls, and 5 red balls. If you pick out three balls, replacing the ball you’ve chosen each time, what’s the probability that all three will be black? (5 pts.) 14. Same urn; again, pick three balls. What’s the probability that they’ll all be white if you don’t replace the balls after picking them? (5 pts.) 15. You and a friend each enter the Pick3 Lotto, picking different numbers between 000 and 999. (You pick 123 and he picks 666, thinking this makes him tough or something.) What’s the probability that at least one of you will win? (5 pts.) 16. Each of us has a 1 in 7 chance of getting arthritis at some point. What are the chances that at least one of Knachel, Miley Cyrus, or Mr. T will eventually suffer from arthritis? (5 pts.) 17. Pick three cards from a deck (don’t replace them after they’re picked; keep them). What’s the probability that all three cards will be of the same suit? (5 pts.) 18. Three friends enroll in a school for wizards. Suppose that this school, unlike some others, assigns students to one of four “houses” randomly. What’s the probability that the three friends will be assigned to the same house? (5 pts.)For these problems involving expected value and utility, carry out the calculations. 19. What is the expected value of a coin flip, where heads wins you $1000 and tails wins you $400? (4 pts.) 20. Assuming a utility function as described by Bernoulli—mapping 1 unit of wealth to 10 units of utility, 2 units of wealth to 30 units of utility, and so on: 3 – 48; 4 – 60; 5 – 70; 6 – 78; 7 – 84; 8 – 90; 9 – 96; 10 – 100—what is the expected utility of the coin flip scenario above? Suppose a choice was offered to someone with this utility function between the coin flip and a guaranteed $700. Would they choose the coin flip, the guarantee, or would they be indifferent? (5 pts.) The following involve Bayes’ Law. Respond as indicated; don’t calculate fully. 21. Our simplest formulation of Bayes’ Law had the same numerator, but the denominator was just ‘P(E)’. We noted that this formula comported well with our intuitions about belief revision. In particular, it captured the fact that implausible hypotheses are relatively hard to support. This is borne out