Wager Mage
Photo by Polina Tankilevitch Pexels Logo Photo: Polina Tankilevitch

What are the odds of rolling a 2 or 3?

Two (6-sided) dice roll probability table Roll a… Probability 2 1/36 (2.778%) 3 2/36 (5.556%) 4 3/36 (8.333%) 5 4/36 (11.111%) 7 more rows

statisticshowto.com - Dice Roll Probability: 6 Sided Dice - Statistics How To
How accurate are spaghetti models?
How accurate are spaghetti models?

Spaghetti Plots Do Not Portray Any Impacts Although most models show possible impacts, to present many models succinctly on a single chart,...

Read More »
Last updated Jan 23, 2020
What is the strangest rule in golf?
What is the strangest rule in golf?

The Flying Insect Rule “If the player's ball lies in a hazard, the insect is considered to be in the hazard and the player may not touch or...

Read More »
Last updated Dec 27, 2018

Contents:

Watch the video for three examples:

Probability: Dice Rolling Examples

Need help with a homework question? Check out our tutoring page!

It’s very common to find questions about dice rolling in probability and statistics. You might be asked the probability of rolling a variety of results for a 6 Sided Dice: five and a seven, a double twelve, or a double-six. While you *could* technically use a formula or two (like a combinations formula), you really have to understand each number that goes into the formula; and that’s not always simple. By far the easiest (visual) way to solve these types of problems (ones that involve finding the probability of rolling a certain combination or set of numbers) is by writing out a sample space.

Dice Roll Probability for 6 Sided Dice: Sample Spaces

A sample space is just the set of all possible results. In simple terms, you have to figure out every possibility for what might happen. With dice rolling, your sample space is going to be every possible dice roll.

Example question: What is the probability of rolling a 4 or 7 for two 6 sided dice?

In order to know what the odds are of rolling a 4 or a 7 from a set of two dice, you first need to find out all the possible combinations. You could roll a double one [1][1], or a one and a two [1][2]. In fact, there are 36 possible combinations.

Dice Rolling Probability: Steps

Step 1: Write out your sample space (i.e. all of the possible results). 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). The rolls that add up to 4 or 7 are in bold:

[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. What I mean by the “size of your sample space” is just all of the possible combinations you listed. In this case, Step 1 had 36 possibilities, so:

9 / 36 = .25

Does Skillz charge a fee?
Does Skillz charge a fee?

Account Monthly Maintenance Fee. If your Account is inactive (i.e. you have not entered at least one (1) tournament) for six (6) consecutive months...

Read More »
Last updated Apr 19, 2021
Is it haram to trade forex?
Is it haram to trade forex?

So, is Forex trading halal or haram? The answer is that it depends on the type of trade you are making. If you are simply exchanging currencies,...

Read More »
Last updated Jun 7, 2021

You’re done!

Back to top

The following table shows the probabilities for rolling a certain number with a two-dice roll. If you want the probabilities of rolling a set of numbers (e.g. a 4 and 7, or 5 and 6), add the probabilities from the table together. For example, if you wanted to know the probability of rolling a 4, or a 7:

3/36 + 6/36 = 9/36.

Roll a… Probability 2 1/36 (2.778%) 3 2/36 (5.556%) 4 3/36 (8.333%) 5 4/36 (11.111%) 6 5/36 (13.889%) 7 6/36 (16.667%) 8 5/36 (13.889%) 9 4/36 (11.111%) 10 3/36 (8.333%) 11 2/36 (5.556%) 12 1/36 (2.778%)

Probability of rolling a certain number or less for two 6-sided dice.

Roll a… Probability 2 1/36 (2.778%) 3 3/36 (8.333%) 4 6/36 (16.667%) 5 10/36 (27.778%) 6 15/36 (41.667%) 7 21/36 (58.333%) 8 26/36 (72.222%) 9 30/36 (83.333%) 10 33/36 (91.667%) 11 35/36 (97.222%) 12 36/36 (100%)

Contents:

1. Probability of a certain number (e.g. roll a 5).

2. Probability of rolling a certain number or less (e.g. roll a 5 or less). 3. Probability of rolling less than a certain number (e.g. roll less than a 5). 4. Probability of rolling a certain number or more (e.g. roll a 5 or more). 5. Probability of rolling more than a certain number (e.g. roll more than a 5). Roll a… Probability 1 1/6 (16.667%) 2 1/6 (16.667%) 3 1/6 (16.667%) 4 1/6 (16.667%) 5 1/6 (16.667%) 6 1/6 (16.667%)

.

Roll a…or less Probability 1 1/6 (16.667%) 2 2/6 (33.333%) 3 3/6 (50.000%) 4 4/6 (66.667%) 5 5/6 (83.333%) 6 6/6 (100%)

.

Roll less than a… Probability 1 0/6 (0%) 2 1/6 (16.667%) 3 2/6 (33.33%) 4 3/6 (50%) 5 4/6 (66.667%) 6 5/6 (83.33%) Roll a…or more Probability 1 6/6(100%) 2 5/6 (83.333%) 3 4/6 (66.667%) 4 3/6 (50%) 5 2/6 (33.333%) 6 1/6 (16.667%) Roll more than a… Probability 1 5/6(83.33%) 2 4/6 (66.67%) 3 3/6 (50%) 4 4/6 (66.667%) 5 1/6 (66.67%) 6 0/6 (0%)

Back to top

Visit out our statistics YouTube channel for hundreds of probability and statistics help videos!

References

Dodge, Y. (2008). The Concise Encyclopedia of Statistics. Springer.

Gonick, L. (1993). The Cartoon Guide to Statistics. HarperPerennial.

Salkind, N. (2016). Statistics for People Who (Think They) Hate Statistics: Using Microsoft Excel 4th Edition.

statisticshowto.com - Dice Roll Probability: 6 Sided Dice - Statistics How To
Are bookies legal in the US?
Are bookies legal in the US?

In 2018, the Supreme Court overturned the federal ban on sports betting, allowing state governments to set their own policies on the matter. 5...

Read More »
Last updated Nov 4, 2022
What do the letters DINK stand for?
What do the letters DINK stand for?

"DINK" is an acronym that stands for "double income, no kids" or "dual income, no kids".

Read More »
Last updated Aug 25, 2020
Who is the most profitable gambler?
Who is the most profitable gambler?

William T. Walters (born July 15, 1946) is an American entrepreneur, philanthropist, and retired professional gambler widely regarded as among the...

Read More »
Last updated Apr 22, 2020
Can my IP address be traced by the police?
Can my IP address be traced by the police?

Police, in particular, often use this feature for tracking criminals and gathering evidence for ongoing or future investigations. So, If you're...

Read More »
Last updated Dec 27, 2018