Advanced Mathematical Decision-Making Probability Project

Waiting for a Double

In many games that use dice, such as Backgammon, players roll 2 dice at a time. Occasionally, this results in what’s known as a double. A double means that the same number shows on both dice, such as two 4’s or two 6’s. Often special rules apply when a player rolls a double. How long does it typically take before a player rolls a double? Here is an experiment we can use to explore this question:

Part I:

1. Roll a pair of dice and continue rolling until you get a double. If you don’t have dice at home, you can roll virtual dice here: https://www.random.org/dice/
2. Record the number of rolls it takes to get a double in the table below.
3. Repeat this experiment with your group a minimum of 10 times.

Trial	Number of rolls it took to get a double
1	Â
2
3
4
5	Â
6
7
8	Â
9
10	Â

Use your data to calculate the experimental probability of rolling a double on a given throw, using the formulas below to help you.

Average # Rolls to get Double = SUM of Number of Rolls = 10

Experimental Probability of rolling Double = 1___ = Average

Part II: List all the possible outcomes of rolling two dice, using the chart to help you. For example, if your first die shows a 2 and your second die shows a 3, you’d write the outcome 2,3. This is different from the outcome 3,2 which would happen if the first die showed 3 and the second showed 2. After you complete the chart, find the theoretical probability of rolling a double, using the formula given below the chart.

POSSIBLE OUTCOMES:

SECOND DIE

123456

FIRST 1 1,1 1,2 1,3 DIE 2 2,1

3 3,1 4
5
6

Theoretical Probability =

Number of Doubles = Total Number of Outcomes

How does your experimental probability compare to the theoretical probability? Are there any differences? Why do you think this is?