从包含 4 个红 5 个蓝和 3 个黑球的袋子中得到一个非红球的概率是多少？
概率是在一种情况的所有可能结果（结果）的集合中，期望结果（结果）发生的可能性。简单来说，概率表示可能性。事件发生的概率表示期望结果与所有可能结果的比率。
概率术语
概率中经常使用不同的术语。实验、试验、事件、互斥事件、结果、有利事件等术语。让我们详细看看它们，
- 实验：实验是指任何具有未定义结果的活动。
- 试验：试验是指一个实验的不同尝试
- 事件：事件是指具有明确结果的试验
- 互斥事件：互斥事件是没有共同点的事件，一个事件的发生会阻止另一个事件的发生。
- 结果：结果是指试验的最终结果
- 有利事件：有利事件是具有期望结果/结果的事件
任何事件发生的概率
任何事件发生概率的正式定义是，有利事件发生的概率/所有事件发生的概率（有利+不利）。概率事件中的事件总集是有利事件和不利事件的总和。这些往往是概率计算比率的分母
从包含 4 个红 5 个蓝和 3 个黑球的袋子中得到一个非红球的概率
解决方案：
figure 1: Bag containing the balls
Number of red balls in the bag = 4
Number of blue balls in the bag = 5
Number of black balls in the bag = 3
Total balls in the bag = 4 + 5 + 3 = 12
Probability of getting a red ball
= Red Balls in the bag/ Total number of Balls in the bag
= 4/12
Probability of getting a blue ball
= Blue Balls in the bag/ Total number of Balls in the bag
= 5/12
Probability of getting a black ball
= Black Balls in the bag/ Total number of Balls in the bag
= 3/12
Now, the Probability of getting a non-red ball can be calculated by three ways:
1st Way:
Probability of getting a non-red ball
= 1 – Probability of getting a red ball
= 1- 4/12
= 8/12
2nd Way:
Probability of getting a non-red ball
= Sum of Probabilities of getting either a Blue ball or a black ball
= Probability of getting a blue ball + Probability of getting a black ball
= 5/12 + 3/12
= 8/12
3rd Way:
Probability of getting a non-red ball
= (Blue Balls in the bag + Black Balls in the bag) / Total number of Balls in the bag
= (5 + 3)/12
= 8/12
Either of the three ways fetches the same result: 8/12 to the above problem.
类似问题
问题 1：从包含 6 个红球和 4 个黑球的袋子中得到一个红球的概率
解决方案：
No of red balls in the bag = 6
No of black balls in the bag = 4
Total balls in the bag = 6 + 4 = 10
Probability of getting a red ball
= Red Balls in the bag/ Total number of Balls in the bag
= 6/10
问题 2：从一副牌中获得国王的概率。
解决方案：
Kings in the Deck = 4
Total No. of cards in the deck = 52
Probability of occurrence of a King from a deck of cards
= Kings in the Deck / Total No. of cards in the deck
= 4/52
问题 3：从包含 3 个红色 3 个蓝色和 4 个黑色球的袋子中得到一个非蓝色球的概率。
解决方案：
No of red balls in the bag = 3
No of blue balls in the bag = 3
No of black balls in the bag = 4
Total balls in the bag= 3 + 3 + 4
Probability of getting a red ball
= Red Balls in the bag/ Total number of Balls in the bag
= 3/10
Probability of getting a blue ball
= Blue Balls in the bag/ Total number of Balls in the bag
= 3/10
Probability of getting a black ball
= Black Balls in the bag/ Total no. of Balls in the bag
= 4/10
Probability of getting a non-blue ball
= 1 – Probability of getting a blue ball
= 1 – 3/10
= 7/10