如何检查六面骰子是否公平？
概率是从概率实验的所有可能结果的集合中得到想要结果的机会。概率实验可以描述为每次尝试都会产生计划外结果的活动。因此，实验的概率是从该实验的所有可能结果中出现期望结果的机会。期望结果和不期望结果的概率之和始终为 1。
期望结果的概率 + 不期望结果的概率 = 1
公平概率
当每个结果发生的机会相等时，概率可以称为公平。在任何一种结果的发生过程中都没有观察到任何偏袒，每个结果都有相同的发生机会。
例如，抛硬币：在这里，正面和反面的每个可能结果都有相同的机会作为结果出现。因此，可以认为抛硬币有资格获得公平的概率。
不公平的概率
当每个结果发生的机会不相等时，概率可以称为不公平。在任何一个结果的发生过程中都会观察到某种偏袒，并且每个结果发生的机会不均等。
例如，抛硬币正面朝上：在这里，硬币的可能结果只有正面，总概率为 1。硬币正面有反面的概率为 0。所以，上述假设硬币的投掷可以被认为有资格获得不公平的概率。
如何检查六面骰子是否公平？
答案：
- Probability when a dice is rolled:
Total number of possible outcomes = 6 (1, 2, 3, 4, 5, 6)
- Probability of having 1 on the roll-up of dice
= Occurrence of 1 on top of dice/ Total number of possible outcomes of dice
= 1/6
- Probability of having 2 on the roll-up of dice
= Occurrence of 2 on top of dice/ Total number of possible outcomes of dice
= 1/6
- Probability of having 3 on the roll-up of dice
= Occurrence of 3 on top of dice/ Total number of possible outcomes of dice
= 1/6
- Probability of having 4 on the roll-up of dice
= Occurrence of 4 on top of dice/ Total number of possible outcomes of dice
= 1/6
- Probability of having 5 on the roll-up of dice
= Occurrence of 5 on top of dice/ Total number of possible outcomes of dice
= 1/6
- Probability of having 6 on the roll-up of dice
= Occurrence of 6 on top of dice/ Total number of possible outcomes of dice
= 1/6
Each of the outcomes of the dice has an equal probability of 1/6. Each outcome is equally likely to come on the top when the dice is rolled. Hence, the rolling of dice can be considered to be a fair probability scenario.
类似问题
问题1：裁判员在比赛开始前掷硬币。它是否符合公平概率？
回答：
When a coin is tossed, there is an equal chance for Heads or Tails to appear. So, it qualifies as a fair probability.
问题 2：考虑一个装有 3 个橙子和 3 个芒果的篮子。 Vaibhav 随机挑选一种水果来吃。这是否符合公平概率情景？
回答：
Since Vaibhav randomly picks the fruit and there is no favoritism shown while choosing the fruit. So, yes it qualifies for a fair probability.
问题 3：启动汽车发动机是否符合公平概率？
回答：
Yes, starting the car engine qualifies for a fair probability as there are two cases of either the car starting or not. And both these outcomes have an equal chance of occurrence. So, it qualifies for a fair probability.
问题 4：事件的结果没有显示出任何偏好的行为。他们是否有资格获得公平概率情景？
回答：
Yes, since there is no partiality towards any particular outcome. The above scenario qualifies for a fair probability scenario.
问题 5：掷出一个公平的骰子。获得奇数的概率是多少？
解决方案：
The odd numbers present on the die is 1, 3, 5.
Therefore, out of the 6 total occurrences, the possible outcomes are 3.
Probability of obtaining an odd number = 3/6 = 1/2.