如果你掷骰子六次，掷出六号的概率是多少？
概率是数学的一部分，它处理事件发生的可能性。就是预测事件发生或不发生的可能性有多大。作为数字的概率仅介于 0 和 1 之间，也可以写成百分比或分数的形式。可能事件 B 的概率通常写为 P(B)。这里 P 表示可能性，B 表示事件的发生。类似地，任何事件的概率通常写为 P()。当事件的最终结果未得到确认时，我们会使用某些结果的概率——它们发生的可能性或它们发生的机会。
虽然概率是从赌博开始的，但在物理科学、商业、生物科学、医学、天气预报等领域，它已经被谨慎地使用了。
为了更准确地理解概率，我们以掷骰子为例：
可能的结果是 - 1、2、3、4、5 和 6。
得到任何结果的概率是 1/6。由于事件发生的可能性是同等可能的事件，因此在这种情况下获得任何数字的可能性相同，它是 1/6 或 50/3%。
概率公式
Probability of an event = {Number of ways it can occur} ⁄ {Total number of outcomes}
P(A) = {Number of ways A occurs} ⁄ {Total number of outcomes}
活动类型
- 同等可能事件：掷骰子后，获得任何可能事件的概率为 1/6。由于该事件是同样可能的事件，因此在这种情况下有可能获得任何数字，它要么是公平掷骰子的 1/6。
- 补充事件：有可能只有两个结果，即一个事件是否会发生。就像一个人会玩或不玩，买笔记本电脑或不买笔记本电脑等都是互补事件的例子。
如果你掷骰子六次，掷出六号的概率是多少？
解决方案：
First you should find the probability that you will NOT get a 6 in order to find the probability that you will get a 6 at least once any of those times. This is much easier.
According to binomial concept
Let’s say P = probability of getting a 6 on each throw = 1/6.
P’ = probability of NOT getting a 6 on each throw is 1-p = 5/6.
When you want to calculate the probability of multiple (unconventional) events happening, you must multiply their independent probabilities (not add them).
So, The probability of not getting a 6 n times = P’ to the nth power.
In this case (5/6)6 = 15,625 / 46,656 ~ 0.334
But the probability we get is of NOT getting a 6 even once. And there are only two possibilities: either we will see it at least once, or never see a 6. So the probability of getting at least one 6 is 1 minus this or about 0.666.
Note: It turns out this probability is roughly the same for any similar problem where you have a 1/n chance for an event and you try n times. In the limit as n approaches infinity, the probability of NOT getting it is 1/e ~ 0.36788. It is interesting that even at n = 6, it is not that far off.
类似问题
问题 1：如果掷骰子 5 次，得到 6 次正好 3 次的概率是多少？
解决方案：
According to binomial concept
The probability of 6 on one roll = 1/6
The probability of 6 on 3 rolls = (1/6)3
The probability of not 6 on one roll = 5/6
The probability of not 6 on 2 rolls = (5/6)2
Ways of selecting 3 from 5 = 5×4/2 =10
So
The probability of exactly 6 on 5 rolls = 10 × (1/6)3 × (5/6)2 = 0.0321
问题2：当你同时掷4个骰子时，至少有一个6的概率是多少？
解决方案：
According to binomial concept
The easiest way to think of this is first to think, “what is the probability of getting no 6’s when you roll 4 die?
In order to roll no 6’s in 4 rolls, you need to know the probability of not rolling a 6 with one dice.
Each 6 sided dice has 5 options that aren’t a 6 (1–5), giving not rolling a 6 a 5/6 chance with one fair dice on one toss.
So the probability of rolling no 6’s with 4 fair die, is (5/6)4.
Therefore, the probability of rolling at least one 6 in 4 roll, is 1-(5/6)4 = 51.775%.
问题 3：如果掷骰子 3 次，得到至少一个 6 的概率是多少？
解决方案：
According to binomial concept
Probability of getting at least one six
= 1 – probability of no six in three roll
Each 6 sided dice has 5 options that aren’t a 6 (1–5),
Giving not rolling a 6, a 5/6 chance with one fair dice on one toss.
So the probability of rolling no 6’s with 3 fair die, is (5/6)3.
= 1 – (5/6)3 = 0.42 (approx)