Question

When you roll two standard six-sided dice, the two dice add up to a quantity between 2 and 12, e.g., 2 & 3 give 5. However, 3 & 2 also give a sum of 5 so there are multiple ways to get a sum of 5. Draw a dot plot for the distribution consisting of all possible dice sums included in the distribution as many times as there are different ways to get that particular sum. That is, make a dot plot where the number of dots above a particular number x matches the number of distinct ways you can roll x as a sum of two dice. How many elements are in this distribution? How is this quantity connected to the six sides per dice and the two dice together? Discuss the shape of the distribution. What is the most common outcome for rolling two standard six-sided dice? Is this surprising based on how Craps is designed in casinos?

          When you roll two standard six-sided dice, the two dice add up
to a quantity between 2 and 12, e.g., 2 & 3 give 5. However, 3
& 2 also give a sum of 5 so there are multiple ways to get a
sum of 5. Draw a dot plot for the distribution consisting of all
possible dice sums included in the distribution as many times as
there are different ways to get that particular sum. That is, make
a dot plot where the number of dots above a particular number x
matches the number of distinct ways you can roll x as a sum of two
dice.
How many elements are in this distribution? How is this
quantity connected to the six sides per dice and the two dice
together?
Discuss the shape of the distribution.
What is the most common outcome for rolling two standard
six-sided dice? Is this surprising based on how Craps is designed
in casinos?

Added by Alex C.

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