As Bernardin (2010) points out, some irrational thinking is the result of trying to
come up with logical explanations for something that is simply due to chance. For
example, when people see a pattern of behavior, they want to generate a logical
explanation for that pattern (Bernardin). People reason that the pattern could not be due
to chance because chance is random and therefore does not follow patterns. However,
people are wrong: Chance, especially in the short run, can create patterns. The following
exercises, inspired by simulations performed by Bernardin, can help your students
understand that chance can produce patterns that do not look random and that chance may
be responsible for variations in human behavior. The simulations overlap so you should
not have the same students do both Simulation A and Simulation B.
Simulation A
Instructions: Pretend that you are playing a basketball game. In this game,
flipping a coin represents taking a shot, getting a “heads” represents making that shot,
and getting a “tails” represents missing that shot. In addition, assume that you will take 5
shots in every quarter of play and that you will take 2 shots in every overtime (OT)
period. Thus, your first 5 flips will represent the 5 shots you would take in the first
quarter.
To get started, get a coin and flip it 5 times. Record the number of heads in your
first 5 flips in the table below. Specifically, put the number of heads in the “Heads
(Makes)” row of the “1st quarter: 1st 5 attempts” column—the square with a blank in it.
Flip the coin 5 more times and record the number of heads for those flips in the “Heads
(Makes)” row of the “2nd quarter: 2nd 5 attempts” column. Keep flipping and recording
until you have results for the 3rd quarter, the 4th quarter, and the two overtime (OT)
periods. Then, add up the total number of heads and put that result in the “Heads” row of
the “Total” column. Finally, fill in the percentage of heads (the “shooting percentage”) by
filling in all the cells in the shaded “Shooting percentage” row. For obtaining the
shooting percentage, you may find the following information helpful: For each quarter, 0
heads = 0%, 1 head = 20%, 2 heads = 40%, 3 heads = 60%, 4 heads = 80%, and 5 heads
= 100%. For the overtimes, 0 heads = 0%, 1 head = 50%, and 2 heads = 100%). For the
“Total” column, 8 heads = 33%, 9 heads = 37%, 10 heads= 42%, 11 heads = 46%, 12
heads = 50%, 13 heads = 54%, 14 heads = 58%, 15 heads = 63%, 16 heads = 67%.
1st
quarter
(1st 5
flips)
Heads
(“Makes”)
Shooting
percentage
2nd
quarter
(2nd 5
flips)
3rd
quarter
(3rd 5
flips)
4th
quarter
(4th 5
flips)
1st OT
(2 flips)
2nd OT
(2 flips)
Total
1. In what quarter or overtime period did you have the highest shooting
percentage? In what quarter or overtime period did you have the lowest
shooting percentage?
2. Can you form a general rule about how likely your coin is to “make” a basket?
3. Would it make sense to try to explain any particular “miss” or “make”?
4. Imagine your data reflected the actual shooting percentages of LeBron James
in a playoff game. How would the announcers explain the variations in
LeBron’s performance?
5. What have you learned from this exercise that you could use for
a. Accepting the newspaper’s explanations for why the stock market
dropped 100 points yesterday?
b. Accepting explanations for why your roommate has been in a bad
mood three days in a row?
c. Accepting the statement that Duke was the best college basketball
team in the country last year because they won the NCAA tournament,
beating Butler 54-52 in the finals?
d. Understanding that to be scientific rather than superstitious, one must
understand how random events affect behavior?
Simulation B
Instructions: Form two teams: Team Jacob and Team Edward. Play a simulated
basketball game by flipping coins. Team Jacob will go first. From then on, take turns. If
the coin comes up heads, your team earns 2 points; if it comes up tails, you get no
additional points. You will record your results on the score sheet at the bottom of the
page by recording your cumulative score in the appropriate boxes. To see how you record
your score, look at the following example.
If Team Jacob started with a “tails,” whereas team Edward started with a “heads,” your
score sheet should look like this:
1st quarter
J 0
E 2
2nd quarter
3rd quarter
4th quarter
Total
If, on the second possession, both team Jacob and Team Edward “scored” (both got a
“heads” when they flipped a coin), the sheet would look like this:
1st quarter
J 0 2
E 2 4
2nd quarter
3rd quarter
4th quarter
Total
If, on the third possession, team Jacob scored but Team Edward did not, the sheet would
look like this:
1st quarter
J 0 2 4
E 2 4 4
2nd quarter
3rd quarter
4th quarter
Total
If the other team makes a run, you may call a 30-second timeout to try to stop that
run-but make a note of what the score was when you called the timeout.
Now, begin your game and record your scores in the box below. Start by letting
Team Jacob flip first. Then, alternate flips until the end of the game.
st
1 quarter
J
E
Official Scoring Sheet
2nd quarter
3rd quarter
4th quarter
Total
1. In what quarter did your team’s offense do best? If this had been a real game
(e.g., between the Celtics and the Lakers) and a team had done well in that
quarter, how would announcers or sportswriters have explained that outcome?
2. In what quarter did your team’s defense do best? If this had been a real game
and a team had done well in that quarter, how would announcers or
sportswriters have explained that outcome?
3. Did you call a time out? Did the time out seem to help? If so, how can you
explain the success of your time out?
4. Explain any streaks that occurred in the game. How much of a role did
momentum play in the game’s outcome?
5. If you lost, how would you explain your loss? If you won, how would you
explain your win?
6. What have you learned from this exercise that you could use for
a. Accepting the newspaper’s explanations for why the stock market
dropped 100 points yesterday?
b. Accepting explanations for why your roommate has been in a bad
mood three days in a row?
c. Accepting the statement that Duke was the best college basketball
team in the country last year because they won the NCAA tournament,
beating Butler 61-59 in the finals?
d. Understanding that to be scientific rather than superstitious, one must
understand how random events affect behavior?