(1) Ask 5 people to make educated guesses about the following two scenarios and record their respoonses (OK to team up with other class members and report the same data):

Question A: Estimate the probability that a rancher from Wyoming who is in the market for a vehicle buys a Toyota.
Question B: Estimate the probability that this rancher buys a Toyota truck.

(a) Report your participants' responses in a table.
(b) According to the laws of probability, should the probability estimate be higher in Question A or Question B? (Note: the laws of probability do allow for the possibility that the two estimates will be equal.  We take that as a given.)
(c) Describe the responses you found.  Were they in accordance with the normative response determined by probability theory?
(d) If you answered "no" to question (c), explain your results.  (Hint: Which heuristic would produce this behavior?)  If you answered "yes" to question (c), explain your results.
(e) Do you think little experiments like this are a valid indicator of people's probabilistic reasoning abilities?  Explain why or why not. (You're being graded on the quality of your explanation, not whether you say "yes" or "no".) Hint: One good answer would appeal to Grice's maxims.  But, there are lots and lots of other good ones!
Extra Credit (worth up to 5 points):  Reverse the order of questions A and B (putting the information about Wyoming , etc. into question B) and ask 5 new people.  Report your results and explain why you think they are similar to your findings in (a), (if they're similar), or, why you think they're different, (if they're different).

(2) Give examples of the use of each of the following heuristics (in a and b) and fallacies (in c and d):
(a) the availability heuristic
(b) the representativeness heuristic
(c) the gambler's fallacy
(d) the conjunction fallacy

(3) (The Allais Paradox)
Tragically, you have just discovered that you suffer from a fatal disease.  Although you are only 25 years old, you will die within the next few months if you do not receive treatment.  However, two new treatments are available that could prolong your life.  The treatments differ in the number of extra  years of life they could grant you and the probability of achieving those extra years of life.  You have the following options:

Option A:
    live 10 years with p = 1.0
Option B:
    live 10 years with p = .89
    live 50 years with p = .10
    live 0 years with p = .01
Option C:
    live 10 years with p = .11
    live 0 years with p = .89
Option D:
    live 50 years with p = .10
    live 0 years with p = .90
(a) Assuming the worth of each possible outcome is the number of years you would live, calculate the expected utility of Option A.
(b) Calculate the expected value of Option B.
(c) Calculate the expected value of Option C.
(d) Calculate the expected value of Option D.
(e) Assuming expected value theory, explain the relationship between Option A and Option C (how would you transform Option A to yield Option C?)
(f)  Assuming expected value theory, explain the relationship between Option B and Option D.

(4) [Note: the sample answer is only illustrative.  Your decision does not have to do with banks or money...]
(a) Give an example of a decision you made -- anytime in the last 4 years -- that involved the consideration of probabilistic information. (e.g. For Dr. Coulson, a good example is the decision to get a new mortgage.)
(b) What was the probabilistic information? (e.g. the probability that interest rates would go up as opposed to down)
(c) In thinking about any of the probabilistic variables involved in your decision, what is one heuristic, bias, or fallacy that could have led you astray? (e.g. Because interest rates have recently been going down, and recent events influence memory more than distant events, use of the availability heuristic might lead you to think that interests rates are likely to go down.)

(5) Is human decision making rational?  Write 1-2 paragraphs that address this question.  Be sure to clearly (but briefly) define what counts as rational, and back up your argument with a brief reference to relevant experimental evidence.  Depending on what your answer is, you may (though you do not have to!) want to provide a reasoned critique of some research in this area.