Department of Mathematics Education
EMAT 6700, J. Wilson
Games
that use Dice
J. Matt Tumlin
You will examine the possible outcomes that occur from throwing a single die and a pair of dice. Many board games, such as Monopoly, use dice to advance players around the playing board. On any throw, each face on a die is equally likely to come up. Since only one face can come up at a time, the results are mutually exclusive.
When you throw two dice, the sum of the dots on the
faces can be anything from 2 through 12.
These sums are not equally likely.
Even though there is only one way to throw a 2 (1+1), there are six ways
to throw a 7 (1+6, 2+5, 3+4, 4+3, 5+2, and 6+1). Thus, the events throwing a 2 and throwing a
7 are not equally likely.
For a Microsoft Word copy, CLICK HERE.
Directions
The materials required for this lab are dice and
calculator. You can have up to six
members per group. Have each member of
the group throw a single die 12 times and pair of dice 12 times and they must
record the results. For a single-die
throw, record the dots on the face that come up. For a two-die throw, record the sum of the
dots on the two faces that come up. For
example, if you throw a 5 and a 3, record an 8.
Make a table similar to that shown below for the data you collect. The single-die throw should list the face
showing and the corresponding frequency for the 12 throws. The two-dice throw should list the sum of the
two faces and the corresponding frequency also for 12 throws.
|
Single-die Throw |
Two-dice Throw
|
||
|
Face Showing |
Corresponding Frequency |
Sum of Faces |
Corresponding Frequency |
|
1 |
2 |
2 |
0 |
|
2 |
3 |
3 |
0 |
|
3 |
1 |
4 |
3 |
|
4 |
2 |
5 |
2 |
|
5 |
2 |
6 |
1 |
|
6 |
2 |
7 |
2 |
|
|
|
8 |
1 |
|
|
|
9 |
1 |
|
|
|
10 |
1 |
|
|
|
11 |
1 |
|
|
|
12 |
0 |
Draw histograms for both the single-die and two-dice
data. Make a table similar to the one
above for your entire group’s data. Draw
histograms of the single-die data for the group and two-dice data for the
group. Make a data table for the entire
class. Draw separate histograms of the
single-die data and the two-dice data for the class. Are there similarities in the three
histograms for the single-die data? Are
there similarities in the three histograms for the two-dice data? How are the histograms of single-die data
different from the histograms of the two-dice data?