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How many ways are there to roll either a 6 or 12 with two dice?

  • Last Updated : 29 Dec, 2021

Probability is also known as the math of chance. This means the possibility, that deals in the occurrence of a likely affair. The value is deputed from zero to one. In math, Probability has been manifest to estimate how likely affairs is to occur. Basically, probability is the extent to which something is to be expected to occur.

Probability

To understand probability more accurately, let’s understand an example of rolling a dice, the possible outcomes are – 1, 2, 3, 4, 5, and 6. The probability of happening any of the likely affairs is 1/6. As the possibility of happening any of the affairs is the same so there is an equal possibility of happening any favorable affair, in this case, it is either of two 1/6 or 50/3.

Formula of Probability

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

DICE

Dice is a tiny brick that has between one and six dots or stains on its border and is used in games to give a random number. Dice are tiny, throwable brick with a noticeable edges that can stop in several figures. They are handed down to give rise to random figures, frequently as part of sideboard games, as well as dice games, board games, role-playing games, and games of chance.

A usual die is a cube with each of its six faces perceptible with a different number 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 favor some results over others for break out or relaxation.

How many ways are there to roll either a 6 or 12 with two dice?

Solution:

There are five ways to have 6 and only one way to obtain 12 on two dices.

Explanation:

When two dices are rolled, there are five possibilities of rolling a sum of 6.

These are (1, 5), (2, 4), (3, 3), (4, 2), (5, 1)

And one possibility of rolling a sum of 12.

These are (6, 6).

Similar Problems

Question 1: How many ways are there to roll either a 7 or 11 with two dice?

Solution:

There are six ways to have 7 and two ways one can have 11 on two dices.

Explanation:

When two dices are rolled, there are six possibilities of rolling a sum of 7.

These are (2, 5), (1, 6), (3, 4), (4, 3), (5, 2), (6, 1).

And two possibilities of rolling a sum of 11.

These are (5, 6), (6, 5).

Question 2: How many ways are there to roll either a 5 or 10 with two dice?

Solution:

There are four ways to have 5 and three ways one can have 10 on two dices.

Explanation:

When two dices are rolled, there are four possibilities of rolling a sum of 5.

These are (1, 4), (2, 3), (3, 2), (4, 1).

And three possibilities of rolling a sum of 10.

These are (4, 6), (5, 5), (6, 4).

Question 3: How many ways are there to roll either a 4 or 9 with two dice?

Solution:

There are three ways to have 4 and four ways to have 9 on two dices.

Explanation:

When two dices are rolled, there are three possibilities of rolling a sum of  4.

These are (1, 3), (2, 2), (3, 1).

And four possibilities of rolling a sum of 9.

These are (3, 6), (4, 5), (5, 4), (6, 3).

Question 4: How many ways are there to roll either a 3 or 8 with two dice?

Solution:

There are two ways to have 3 and five ways one can have 8 on two dices.

Explanation:

When two dices are rolled, there are two possibilities of rolling a sum of 3.

These are (1, 2), (2, 1).

And five possibilities of rolling a sum of 8.

These are (2, 6), (3, 5), (4, 4), (6, 2), (5, 3).

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