Probability: Dice Rolling

Probability 6 Comments

It’s common to find questions about dice rolling in probability and statistics. You might be asked the probability of rolling a five and a seven, or rolling a twelve. By far the easiest (visual) way to solve these types of problems (finding the probability of rolling a certain combination or set of numbers) is by writing out a sample space.

A sample space is the set of all possible probabilities. For example, in order to know what the odds are of rolling a 4 or a 7 from a set of two dice, we would first need to find out what all the possible combinations are. We could roll a double one [1][1], or a one and a two [1][2]. In fact, there are 36 possible combinations.

Step 1: Write out your sample space. For two dice,  the 36 different possibilities are:

[1][1], [1][2], [1][3], [1][4], [1][5], [1][6],
[2][1], [2][2], [2][3], [2][4], [2][5], [2][6],
[3][1], [3][2], [3][3], [3][4], [3][5], [3][6],
[4][1], [4][2], [4][3], [4][4], [4][5], [4][6],
[5][1], [5][2], [5][3], [5][4], [5][5], [5][6],
[6][1], [6][2], [6][3], [6][4], [6][5], [6][6]

Step 2: Look at your sample space and find how many add up to 4 or 7 (because we’re looking for the probability of rolling one of those numbers).

[1][1], [1][2], [1][3], [1][4], [1][5], [1][6],
[2][1], [2][2], [2][3], [2][4],[2][5], [2][6],
[3][1], [3][2], [3][3], [3][4], [3][5], [3][6],
[4][1], [4][2], [4][3], [4][4], [4][5], [4][6],
[5][1], [5][2], [5][3], [5][4], [5][5], [5][6],
[6][1], [6][2], [6][3], [6][4], [6][5], [6][6].

There are 9 possible combinations.

Step 3: Take the answer from step 2, and divide it by the size of your total sample space from step 1:

9 / 36 = .25

You’re done!

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6 Responses to “Probability: Dice Rolling”

  1. Karin Martindale said:

    Sep 22, 09 at 11:50 am

    I saw in the textbook the page where sample space was explained in Chapter 2, but it only listed it for a problem that had 6 outcomes. It was nice to see this post with a possible 36 outcomes because it showed me how to complete a more complex scenario without being confusing.

  2. Angie Widdows said:

    Sep 22, 09 at 6:15 pm

    This post was very helpful. I never thought of actually writing out the problem with the actual dice rolls. It helos you to visualize the problem and then actually solve it in a way that you can understand.

  3. Rebecca Gamble said:

    Sep 22, 09 at 11:32 pm

    These types of problems are all in chapter 3 and 2. The brake down of these steps make you think “how could I’ve gotten that wrong?” thank you

  4. Kalynn Grabau said:

    Sep 23, 09 at 8:00 am

    I definately needed this in order to understand the homework!! Thanks so much, now it’s making sense.

  5. Mary Johnson said:

    Sep 23, 09 at 2:34 pm

    since this seemed to help everyone else I am going to practice it. It does seem to make it a little easier to understand.

  6. Catherine Flanagan said:

    Sep 26, 09 at 8:14 pm

    This blog helped me a lot to understand probabilities of dice rolling. I agree with Rebecca…how could I have gotten the question wrong?

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