掷一对骰子时得到 5 或 6 的概率是多少？

概率是事件发生可能性的数值描述。事件的概率在 0 到 1 的范围内，其中 0 表示事件的不可能性，1 表示事情的确定性。概率越高，事件发生的机会就越大。

概率中使用的术语

概率中使用的术语是实验、随机实验、样本空间、结果和事件。让我们简要地看一下这些术语的定义，

• 实验：产生某些结果的操作。

Example When we throw a die, there will be 6 numbers from which anyone can be up. So, the operation of rolling a die may be said to have 6 outcomes.

• 随机实验：一种操作，其中所有可能的结果都是已知的，但确切的结果是不可预测的。

Example When we throw a die there can be 6 outcomes but we cannot say the exact number which will show up.

• 样本空间：操作的所有可能结果。

Example When we throw a die there can be six possible outcomes that is from {1,2,3,4,5,6} and represented by S.

• 结果：样本空间 S 之外的任何可能结果。

Example When we throw a die, we might get 6.

• 事件：当结果属于事件时必须发生的样本空间的子集，由 E 表示。

Example When we roll a die there are six sample spaces {1, 2, 3, 4, 5, 6}. Let’s E occurs when “number is divisible by 2” then E ={2, 4, 6}. If the outcome is {2} which is a subset of E so it is considered an event that occurs otherwise event does not occur. Let’s look at the formula for an event occurring,

Probability of an event occur = Number of outcomes / Sample Space

掷一对骰子时得到 5 或 6 的概率是多少？

解决方案：

Sample Space of one dice = 6

Sample Space of 2 dice = 6 × 6 = 36

Number of outcomes for sum of 5 = 4 {(1, 4), (2, 3), (3, 2), (4, 1)}

Number of outcomes for sum of 6 = 5 {(1, 5), (2, 4), (3, 3), (4, 2), (5, 1)}

Total Outcomes = 4 + 5 = 9

Probability of getting a sum of 5 or 6 = 9/36 = 1/4.

示例问题

问题 1：同时抛两个硬币时至少（最少）一个正面的概率。

解决方案：

Sample Space of one coin = 2

Sample Space of 2 coins = 2 × 2= 4

Number of outcomes for at least one head = 3 {(H, T),(T, H),(H, H)}

Probability of getting at least one head = 3/4.

问题2：掷两个骰子得到偶数和的概率。

解决方案：

Sample Space of one dice = 6

Sample Space of 2 dice = 6 × 6 = 36

Number of outcomes to get a sum of even = 18 ((1, 1),(1, 3),(1, 5),(2, 2),(2, 4),(2, 6),(3, 1),(3, 3),(3, 5),(4, 2),(4, 4),(4, 6),(5, 1),(5, 3),(5, 5),(6, 2),(6, 4),(6, 6))

Probability of getting a sum of even number = 18/36 = 1/2.

问题 3：掷两个骰子时得到 4 的倍数之和的概率。

解决方案：

Sample Space of one dice = 6

Sample Space of 2 dice = 6 × 6 = 36

Number of outcomes to get a sum of multiple of 4 = 9 ((1, 3),(2, 2),(2, 6),(3, 1),(3, 5),(4, 4),(5, 3),(6, 2),(6, 6))

Probability of getting a sum of multiple of 4 = 9/36 = 1/4.

问题 4：掷两个骰子得到 6 的概率。

解决方案：

Sample Space of one dice = 6

Sample Space of 2 dice = 6 × 6 = 36

Number of outcomes to get a product of 6 = 4 ((1, 6),(2, 3),(3, 2),(6, 1))

Probability of getting a product of 6 = 4/36 = 1/9.