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How to calculate Dice Probabilities?

  • Last Updated : 12 May, 2022

Probability is also known as a possibility, which works in the happening of a likely event. The utility is designated from zero to one. In math, Probability has been obvious to approximate how possible events are to occur. Basically, the probability is the scope to which something is to be expected to take place.


To understand probability more exactly, let’s understand an example of flipping a coin, the possible outcomes are – head and tail. The possibility of happening any of the likely events is 1/2. As the possibility of occurring any of the likely events is the same so there is an equal possibility of happening any favorable affair, in this case, it is 1/2.

Formula of Probability

P(A) = {Number of affair A} ⁄ {Total number of affair}


Dice is a small block that has between one and six mark or tint on its boundary and is used in games to give a randomly integer. Dice are small, tossable blocks with a detectable boundary that can stop in respective figures. They are handed down to give stand-up to respective figures, often as part of sideboard games, as well as dice games, board games, role-playing games, and games of chance.

A usual die is a block with each of its six sides detectable with a different integers of figures from one to six. When throwable or rolled, the die comes to pause shows a random number from one to six on its higher side, with the happening of each affair being equally likely. Dice may also have concave or unequal shapes and may have faces noticeable with figures or characters instead of the pit. Filled dice are drawn to favour some results over others for break out or relaxation.

How to calculate Dice Probabilities?


  • One Dice Rolls

The uncomplicated and easiest case of dice probabilities is the possibility of occurring a specific integer with one dice. In probability, the primary act is that one must compute it by looking at the number of likely events in collation to the desired events.

Dice presents six likely events. Furthermore, the attentiveness of the independent would be only for one affair disregarding of the choice of integer. A dice probability calculator would be totally convenient in this regard.

The formula one may use in this case is,

P(A) = {Number of affair to A} ⁄ {Total number of affair}

Therefore, the odds of getting a specif

umber, if the number is 6, this gives,

Probability = 1 ÷ 6 = 0.167

Probabilities are accessible as numbers between no possibility and reliability. Furthermore, no possibility resembles 0 and reliability resembles 1. An independent can multiply this by 100 to operate a percentage. As a consequence, the possibility of getting 6 on the dice is 16.7%.

  • Two or More Dice

The probabilities definitely get a little more complex to work out when two dice are concerned. The calculation of uncommon probabilities takes place when one wish to know the probability of getting two 6s by throwing two dice. Most remarkable, the result of one dice does not rely upon on the result of the other dice.

Unconventional probabilities have the rule that one must multiply the individual probabilities jointly to attain the outcome. Therefore, the formula for this is,

Probability of both = Probability of result one × Probability of result two

  • Total Score from Two or More Dice

If an individual wants to know the likelihood of getting a particular total sore by rolling two or more dice, then one must go back to the simple rule.

This simple rule is probability = number of likely result divided by the number of likely results. Again, the use of a dice probability calculator is critical here. Calculating the number of result one is concerned in requires more work. If an individualistic wish a total score of 4 on two dice, then this is attainable by rolling 1 and 3, 3 and 1, or 2 and 2.

Furthermore, the individual must observe the dice individually, 1 on first dice and 3 on other dice is surely different than a 3 on first dice and 1 on the second dice. For rolling a 4, there are three ways to get the result one wishes. Hence, there are 36 likely result. The work out of this is as follows,

Probability = Number of desired outcomes/Number of possible outcomes = 3 ÷ 36 = 0.0833.

The proportion comes out to be 8.33 percent. Also, 7 is the most favourable  outcome for two dice. In addition, there are six ways to attain it. The probabilit

this case is 6 ÷ 36 = 0.167 = 16.7%.

Similar Problems

Question 1: Find the probability of retrieving a sum of 8 on throwing two dice?


There are 36 total likely results on throwing two dice i.e., 6² = 6 × 6 = 36.

There are 5 total possibility of retrieving a sum of 8 on throwing two dice i.e., (2, 6), (3, 5), (4, 4), (5, 2), (6, 2).

Hence, the probability of retrieve a sum of 8 on throwing two dice is 5/36.

Question 2: Shawn tosses a die 400 times and he documents the score of getting 6 as 30 times. What could be the probability of

a) retrieving a score of 6?

b) retrieving a score under 6?


a) P (getting a score of 6)  

= Number of times getting 6/total times

= 30/400

= 3/40

b) P (getting a score under 6)

= number of times getting under 6/total times

= 370/400

= 37/40

a) P (getting 5) = 3/40

b) P (getting under 6) = 37/40

Question 3: What is the probability of retrieving a sum of 6 if two dice are thrown?


When two dice are rolled, n(S) = 36. Let, A be the event of getting a sum of 6. Then,

A = {(3, 3), (2, 4), (4, 2), (1, 5), (5, 1)}

n(A) = 5

Hence, the required probability will be,

P(A) = n(A)/n(S) = 5/36.

Question 4: Find the probability of throwing two dice and retrieving a sum of 4.


The set of possible outcomes when we roll a die are {1, 2, 3, 4, 5, 6}

So, when two dice are rolled, there are 6 × 6 = 36 chances.

When we roll two dice, the probability of retrieving number 4 is (1, 3), (2, 2), and (3, 1).

So, the number of favorable outcomes = 3

Total number of possibilities = 36

Probability = {Number of likely affair } ⁄ {Total number of affair} = 3 / 36 = 1/12.

Thus, 1/12 is the probability of rolling two dice and retrieving a sum of 4.

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