Appendix F
F PROBLEM SET 4, 2002
Problem 1
A skier knows from past experience that she can run a particular course in under 2
minutes 15 seconds about 40% of the time. To qualify for an upcoming race, she must
choose one of two options:
a.) Run the course only once, completing it in less than 2 minutes 15 seconds.
b.) Run the course three times and complete it in an average of less than 2
minutes 15 seconds.
Which option should she choose to give herself the best chance of qualifying?
Figure F-1. The Skier Problem.
Problem 2
An ordinary deck of 52 playing cards is randomly shuffled and four cards are dealt from the
deck (without replacing them). Of the following two outcomes, which is more likely?
a)
A_ 3_ 9_ Q_
b)
A_ 3_ 9_ Q_
c) Both are equally likely.
d) It is not possible to answer this question.
Figure F-2. Hearts and diamonds were colored red in original.
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Problem 3
Suppose someone spins the spinner at
the right ten times in a row. Of the
following possible outcomes, which is
most likely to occur?
a) The spinner will land on blue five
times and on green five times.
b) The spinner will land on blue seven
times and on green three times.
c) The spinner will land on blue all ten
times.
d) All of the above are equally likely.
e) It is not possible to answer this
question.
Now suppose the same spinner is spun 500 times. Each time it is spun, the color on which
it lands is recorded on a separate slip of paper as either “B” for blue or “G” for green. All
five hundred slips of paper are put into a box and mixed thoroughly. Ten slips are drawn
from the box at random. Of the following possible outcomes, which is most likely to
occur?
a) Five of the slips say “B” and five says “G.”
b) Seven of the slips say “B” and three say “G.”
c) All ten of the slips say “B.”
d) All of the above are equally likely.
e) It is not possible to answer this question.
Figure F-3. The Binomial Spinner Problem and the Box Problem.
The original spinner face had seven blue and three green sectors.
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Problem 4
A food critic for a major newspaper determines his restaurant reviews by visiting a
restaurant and randomly choosing an entree from that night’s menu. After writing such
reviews for a year, the critic believed that when he returned to visit restaurants that he
originally reviewed very positively, he usually did not find the food quite as good as he did
during his first visit.
What do you think best explains the critic’s experience?
Figure F-4.
Problem 5
The game of squash can be played either to 9 points or to 15 points. Christina does not
play squash as well as her friend Angela. Is it to Christina’s advantage to prefer either
scoring system over the other when she plays against Angela?
Figure F-5. The Squash Problem. Adapted from Kahneman and
Tversky (1982).
Problem 6
How many patterned stacks of cubes can you make if each stack is four cubes high and you
have as many black cubes and white cubes as you need?
Figure F-6. Adapted from Davis and Maher (1997).
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Problem 7
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. As you know,
about 50% of all babies are boys. The exact percentage of boys, however, varies from day
to day. Sometimes it may be higher than 50%, sometimes lower.
For a period of one year, each hospital recorded the days on which less than 40% of the
babies born were boys. Which hospital do you think recorded more such days?
a.) The larger hospital
b.) The smaller hospital
c.) About the same
d.) It is not possible to answer this question.
Figure F-7. The Hospital Problem. Adapted from Well et al.
(1990), after Kahneman and Tversky (1972).
Problem 8
When they turn 18, American males must register for the draft at the local post office. In
addition to other information, the height of each male is recorded. The national average
height of 18-year-old males is 5 feet 9 inches.
Every day for one year, 25 men registered at post office A and 100 men registered at post
office B. At the end of each day, a clerk kept a record of the tallest person to register in
either of the post offices that day.
Which would you expect to be true? (circle one)
1. The number of days on which Post Office A had the tallest person registering
was greater than that of Post Office B.
2. The number of days on which Post Office B had the tallest person registering
was greater than that of Post Office A.
3. There is no reason to think that the number of days on which one post office
had the tallest person registering was greater than that of the other post office.
4. It is not possible to answer this question.
Figure F-8. The Tallest Person Problem. Adapted from Well
et al. (1990), after Kahneman and Tversky (1972).
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