B. You've reserved a seat for a Broadway play for which the ticket price is $40. As you enter the theater to buy your ticket, you discover you've lost $40 from your pocket. Would you still buy the ticket? (Assume you still have enough left to do so.)

C. Linda is 31, single, outspoken, and very
bright. She majored in philosophy in college. As a student, she was deeply
concerned with discrimination and other social issues, and participated
in anti-nuclear demonstrations. Which statement is more likely?

- a. Linda is a bank teller.

b. Linda is a bank teller and active in the feminist movement.

E. A certain town is served by two hospitals.
In the larger hospital about 45 babies are born each day, and in the smaller
hospital about 15 babies are born each day. Although the overall proportion
of boys is about 50%, that actual proportion at either hospital may be
greater or less that 50% on any given day. At the end of the year, which
hospital will have the greater number of days on which more that 60% of
the babies born were boys?

- a. the large hospital

b. the small hospital

c. neither, it is equally probable

G. Choose between

- a) a sure gain of $3000, and

b) an 80% chance of winning $4000 and a 20%
chance of winning nothing

I. Threatened by a superior force, the general has to choose between two escape routes. Her aides tell her that if she takes the first, 400 soldiers will die. If she takes the second, there's a one-third chance that no soldier will die, and a two-thirds chance that 600 soldiers will die. Which route should she take?

J. Choose between

- a) a sure loss of $3000, and

b) an 80% chance of losing $4000 and a 20% chance of losing nothing

B. These heuristic are often very useful
but sometimes they lead to systematic errors.

B. The heuristic is useful in inductive reasoning. For example, if we want to know how likely it is that Jones will pass the course we might consider the degree to which Jones represents that group of students who pass.

C. The use of this heuristic can, however, systematically lead one to make poor judgements in some circumstances.

- 1. Sometimes the manner in which the object
or event is represented makes one insensitive to the prior probabilities
involved.

2. Sometimes the manner in which the object or event is represented leads one to ignore the basic rules of the probability calculus, e.g., that the likelihood of a conjunction is always less than the likelihood of each conjunct taken singly.

3. Sometimes the manner in which the object or event is represented makes one insensitive to the fact that small samples are less representative than large samples are.

4. Sometimes the manner in which the object or event is represented leads one to misconceive the outcome of chance. For example, some outcomes of a random selection are taken to "look more random" than equally likely alternatives.

5. Sometimes the manner in which the object or event is represented makes one insensitive to the fact that, in circumstances in which random events cluster around a mean or average, extraordinary events are likely to be followed by more ordinary ones (regression to the mean). People tend to think that extreme instances are representative of future instances.

B. This heuristic is useful in inductive reasoning because (1) typically instances of large classes are recalled better and faster than instances of small groups, (2) likely events are often easier to imagine, (3) causal connections are repeatable and therefore more likely to be remembered. When the availability is associated with the objective likelihood of an event, this heuristic is trustworthy.

C. The use of this heuristic can, however, systematically lead one to make poor judgements in some circumstances.

- 1. A class whose instances are readily available
might appear to be more numerous than it is.

2. Events that easily come to mind might be judged more likely than they are.

3. The availability of certain information may be biased because one has had limited exposure to events of a certain kind, or because the events are more graphic, remarkable or noticable and attract more attention, or because one has stored the information in a particular fashion.

B. Insufficient adjustment due to anchoring can lead to mistakes.

- 1. Sometimes reasoners hold fast to some
piece of information and ignore the consequences of additional information.

2. When solving a problem involving probabilities, reasoners may start with an initial value and adjust it to reach a final value. The anchoring phenomenon results when their results are biased toward the initial value.

3. Sometimes reasoners anchor to an initial problem-solving method when a change in methods would be recommended.

B. But studies show that people would rather take a risk than suffer a loss. Equivalent problems get different responses depending on whether the problem is framed in terms of losses or gains.