两个骰子同时掷出的最大总和是多少？

概率也称为可能性。这意味着机会的数学，即可能发生的事件的交易。该值被指定为从零到一。在数学中，概率已被证明可以猜测事件发生的可能性。基本上，概率是预期某事发生的范围。

可能性

为了更正确地理解概率，以掷骰子为例，可能的结果是 - 1、2、3、4、5 和 6。出现任何有利结果的可能性是 1/6。由于发生任何事件的概率是相同的，因此得到任何可能数字的概率相似，在这种情况下，它是 1/6 或 50/3。

概率公式

Probability of an event = {Number of favourable events } ⁄ {number of total events}

P(A) = {Number of ways A occurs} ⁄ {Total number of events}

骰子

骰子是一个小方块，边缘有 1 到 6 个标记或点，在游戏中用于给出随机数字。骰子是小的、可投掷的块，带有标记的边，可以在几个数字中暂停。它们被用来产生随机数字，通常作为备牌游戏以及骰子游戏、棋盘游戏、角色扮演游戏和机会游戏的一部分。

一个惯用的骰子是一个立方体，它的六个面中的每一个面都带有从一到六个不同数量的图形。当可投掷或滚动时，骰子会暂停，在其较高的一侧出现一个从 1 到 6 的随机数，每个事件的发生概率相同。骰子也可能有凹形或不均匀的形状，并且可能有用数字或字符而不是点子标记的面。加载的骰子被抽出来以服务于某些结果而不是其他结果，以用于逃避或娱乐。

两个骰子同时掷出的最大总和是多少？

解决方案：

Possibility for throwing six sided two dice will be 1, 2, 3, 4, 5 and 6 faces in each (two) dice.

Two dice are roll at the same time, number of attainable outcome can be 6² = (6 × 6 ) = 36 because each die has 1 to 6 number on its dots.

Now, let’s consider the possible sums from rolling two dice. The smallest possible sum happens when all of the dice are the smallest, or one each. This gives a sum of two when two dice are thrown i.e., (1, 1). The greatest number on a die is six, which means that the greatest possible sum happens when all two dice are sixes is 12 i.e., (6, 6).

When n dice are rolled, the minimal attainable sum is n and the greatest attainable sum is 6n.

There is only one way when two dice can total 2,

• 2 ways for 3
• 3 ways for 4
• 4 ways for 5
• 5 ways for 6
• 6 ways for 7
• 5 ways for 8
• 4 ways for 9
• 3 ways for 10
• 2 ways for 11
• 1 ways for 12

Forming Sums,

As shown above, for two dice the possible sums include every number from 2 to 12.

Maximum total outcome of the two faces of the dice is (6, 6) = 6 + 6 = 12

The probability of obtaining maximum total outcome of the two faces of the dice = 1/36

类似问题

问题 1：当掷出两个骰子时，骰子的两个面共得到 10 的概率是多少？

解决方案：

Possibility for throwing six sided two dice will be 1, 2, 3, 4, 5 and 6 faces in each (two) dies.

Two dice are roll at the same time, number of attainable outcome can be 6²= (6 × 6 ) = 36 because each die has 1 to 6 number on its dots.

Now, let’s consider the possible sums from rolling two dice. The smallest possible sum happens when all of the dice are the smallest, or one each. This gives a sum of two when two dice are thrown i.e., (1, 1). The greatest number on a die is six, which means that the greatest possible sum happens when all two dice are sixes is 12 i.e., (6, 6).

When n dice are rolled, the minimal attainable sum is n and the greatest attainable sum is 6n.

There is only one way when two dice can total 2,

• 2 ways for 3
• 3 ways for 4
• 4 ways for 5
• 5 ways for 6
• 6 ways for 7
• 5 ways for 8
• 4 ways for 9
• 3 ways for 10
• 2 ways for 11
• 1 ways for 12

Forming Sums,

As shown above, for two dice the possible sums include every number from 2 to 12.

The possibility of getting a total of 10 on the two face of the dice will be (5, 5) (6, 4) (4, 6) 

Probability = 3/36

问题2：当掷出三个骰子时，骰子三个面的最大总和是多少？

解决方案：

Possibility for throwing six sided three dice will be 1, 2, 3, 4, 5 and 6 dots in each (three) dies.

Three dice are roll at the same time, number of attainable outcome can be 6³ = (6 × 6 × 6) = 216 because each die has 1 to 6 number on its dots.

Now, let’s consider the possible sums from rolling three dice. The smallest possible sum happens when all of the dice are the smallest, or one each. This gives a sum of three when three dice are thrown i.e., (1, 1, 1). The greatest number on a die is six, which means that the greatest possible sum happens when all three dice are sixes is 18 i.e., (6, 6, 6).

When n dice are rolled, the minimal attainable sum is n and the greatest attainable sum is 6n.

There is only one way when three dice can total 3,

• 3 ways for 4
• 6 ways for 5
• 10 ways for 6
• 15 ways for 7
• 21 ways for 8
• 25 ways for 9
• 27 ways for 10
• 27 ways for 11
• 25 ways for 12
• 21 ways for 13
• 15 ways for 14
• 10 ways for 15
• 6 ways for 16
• 3 ways for 17
• 1 ways for 18

Forming Sums,

As shown above, for three dice the possible sums include every number from three to 18.

Maximum total outcome of the three face die is (6, 6, 6) = 6 + 6 + 6 = 18

Probability = 1/216

问题 3：当掷出两个骰子时，骰子的两个面共得到 5 的可能性有多大？

解决方案：

Possibility for throwing six sided two dice will be 1, 2, 3, 4, 5 and 6 faces in each (two) dies.

Two dice are roll at the same time, number of attainable outcome can be 6² = (6 × 6 ) = 36 because each die has 1 to 6 number on its dots.

Now, let’s consider the possible sums from rolling two dice. The smallest possible sum happens when all of the dice are the smallest, or one each. This gives a sum of two when we are throwing two dice i.e., (1, 1). The greatest number on a die is six, which means that the greatest possible sum happens when all two dice are sixes is 12 i.e., (6, 6).

When n dice are rolled, the minimal attainable sum is n and the greatest attainable sum is 6n.

There is only one way when two dice can total 2,

• 2 ways for 3
• 3 ways for 4
• 4 ways for 5
• 5 ways for 6
• 6 ways for 7
• 5 ways for 8
• 4 ways for 9
• 3 ways for 10
• 2 ways for 11
• 1 ways for 12

Forming Sums,

As shown above, for two dice the possible sums include every number from 2 to 12.

The possibility of getting a total of 5 on the two face of the dice will be (4, 1), (1, 4), (2, 3), (3, 2). 

Probability = 4/36

问题4：当掷出三个骰子时，骰子的三个面共得到17的可能性有多大？

解决方案：

Possibility for throwing six sided three dice will be 1, 2, 3, 4, 5 and 6 dots in each (three) dies.

Three dice are roll at the same time, number of attainable outcome can be 6³ = (6 × 6 × 6) = 216 because each die has 1 to 6 number on its dots.

Now, let’s consider the possible sums from rolling three dice. The smallest possible sum happens when all of the dice are the smallest, or one each. This gives a sum of three when three dice are thrown i.e., (1, 1, 1). The greatest number on a die is six, which means that the greatest possible sum happens when all three dice are sixes is 18 i.e., (6, 6, 6).

When n dice are rolled, the minimal attainable sum is n and the greatest attainable sum is 6n.

There is only one way when three dice can total 3,

• 3 ways for 4
• 6 ways for 5
• 10 ways for 6
• 15 ways for 7
• 21 ways for 8
• 25 ways for 9
• 27 ways for 10
• 27 ways for 11
• 25 ways for 12
• 21 ways for 13
• 15 ways for 14
• 10 ways for 15
• 6 ways for 16
• 3 ways for 17
• 1 ways for 18

Forming Sums,

As shown above, for three dice the possible sums include every number from three to 18

The possibility of getting a total of 17 on the three face of the dice will be (6, 6, 5) (6, 5, 6) (5, 6, 6)

Probability = 3/216

问题 5：当掷出两个骰子时，骰子的两个面共有 12 点的可能性有多大？

解决方案：

Possibility for throwing six sided two dice will be 1, 2, 3, 4, 5 and 6 faces in each (two) dies.

Two dice are roll at the same time, number of attainable outcome can be 6²= (6 × 6 ) = 36 because each die has 1 to 6 number on its dots.

Now, let’s consider the possible sums from rolling two dice. The smallest possible sum happens when all of the dice are the smallest, or one each. This gives a sum of two when two dice are thrown i.e., (1, 1). The greatest number on a die is six, which means that the greatest possible sum happens when all two dice are sixes is 12 i.e., (6, 6).

When n dice are rolled, the minimal attainable sum is n and the greatest attainable sum is 6n.

There is only one way when two dice can total 2,

• 2 ways for 3
• 3 ways for 4
• 4 ways for 5
• 5 ways for 6
• 6 ways for 7
• 5 ways for 8
• 4 ways for 9
• 3 ways for 10
• 2 ways for 11
• 1 ways for 12

Forming Sums,

As shown above, for two dice the possible sums include every number from 2 to 12.

There is only one possibility to obtain a total of 12 on the two face of the dice will be (6, 6)

Probability = 1/36