If i roll two dice, what is the probability that neither of them are prime nor even?

Probability is a part of mathematics that deals with the possibility of happening of events. It is to forecast that what are the possible chances that the events will occur or the event will not occur. The probability as a number lies between 0 and 1 only and can also be written in the form of a percentage or fraction. The probability of likely event A is often written as P(A). Here P shows the possibility and A shows the happening of an event. Similarly, the probability of any event is often written as P(). When the end outcome of an event is not confirmed we use the probabilities of certain outcomes—how likely they occur or what are the chances of their occurring.

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Similar Problems
Dice roll probability: 6 Sided Dice Example
Dice Roll Probability for 6 Sided Dice: Sample Spaces
Dice Rolling Probability: Steps
Two (6-sided) dice roll probability table
Dice Roll Probability Tables
Probability of a certain number with a Single Die.
Probability of rolling a certain number or less with one die
Probability of rolling less than certain number with one die
Probability of rolling a certain number or more.
Probability of rolling more than a certain number (e.g. roll more than a 5).

To understand probability more accurately we take an example as rolling a dice:

The possible outcomes are — 1, 2, 3, 4, 5, and 6.

The probability of getting any of the outcomes is 1/6. As the possibility of happening of an event is an equally likely event so there are same chances of getting any number in this case it is either 1/6 or 50/3%.

Formula of Probability

Probability of an event, P(A) = (Number of ways it can occur) ⁄ (Total number of outcomes)

Types of Events

Equally Likely Events: After rolling dice, the probability of getting any of the likely events is 1/6. As the event is an equally likely event so there is same possibility of getting any number in this case it is either 1/6 in fair dice rolling.
Complementary Events: There is a possibility of only two outcomes which is an event will occur or not. Like a person will play or not play, buying a laptop or not buying a laptop, etc. are examples of complementary events.

Answer:

A standard die has six sides numbering 1, 2, 3, 4, 5, and 6. If the die is fair, then each of these outcomes is equally likely event. Since there are six possible outcomes. The probability of getting any side of the die is 1/6. The probability of obtaining a 1 is 1/6, the probability of obtaining a 2 is 1/6, and so on.
The number of total possible outcomes is equal to the total numbers of the first die (6) multiplied by the total numbers of the second die (6), which is 36. So, the total possible outcomes when two dice are thrown together is 36.
The equally likely outcomes of rolling two dice are shown below:
(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)

Dice roll probability: 6 Sided Dice Example

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

You’re done!
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Two (6-sided) dice roll probability table

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%)

Dice Roll Probability Tables

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).

Probability of a certain number with a Single Die.

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%)

Probability of rolling a certain number or less with one die

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%)

Probability of rolling less than certain number with one die

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%)

Probability of rolling a certain number or more.

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%)

Probability of rolling more than a certain number (e.g. roll more than a 5).

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%)

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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.

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