Statistics of Dice Throw

骰子投掷的统计

The probababilities of different numbers obtained by the throw of two dice offer a good introduction to the ideas of probability. For the throw of a single die, all outcomes are equally probable. But in the throw of two dice, the different possibilities for the total of the two dice are not equally probable because there are more ways to get some numbers than others. There are six ways to get a total of 7, but only one way to get 2, so the "odds" of getting a 7 are six times those for getting "snake eyes". This simple example raises the idea of distinguishable states. For example, throwing a 3 is twice as likely as throwing a 2 because there are two distinguishable ways to get a 3.

掷两个骰子得到的不同点数的概率提供了一个概率概念的良好介绍。对于掷一个骰子的情况，所有结果都是等概率的。但掷两个骰子时，两个骰子点数之和的不同可能性并不等概率，因为有些数的出现方式比其他数更多。例如，得到总和为7的方式有六种，而得到2的方式只有一种，因此得到7的概率是得到“双一”（snake eyes）的六倍。这个简单的例子引出了可区分状态的概念。例如，得到3的概率是得到2的两倍，因为有两种可区分的方式得到3。

The probability of getting a given value for the total on the dice may be calculated by taking the total number of ways that value can be produced and dividing it by the total number of distinguishable outcomes. So the probability of a 7 on the dice is 1/6 because it can be produced in 6 ways out of a total of 36 possible outcomes.

掷骰子得到特定总点数的概率可以通过将该点数能产生的总方式数除以所有可区分的结果总数来计算。因此，掷出点数7的概率是1/6，因为它可以在36种可能的结果中以6种方式产生。

Of Dice and the Binomial Distribution

骰子与二项分布

The throw of a die or the picking of a card out of a deck are perhaps the most visible examples of the statistics of random events. Most of the conceptual tasks in probability for these kind of events can be handled with the binomial distribution. The binomial distribution

掷骰子或从一副牌中抽一张牌可能是随机事件统计学中最直观的例子。对于这类事件的概率概念任务，大多数都可以用二项分布来处理。二项分布

can serve as a kind of "multi-tool" for common statistical questions.

可以作为解决常见统计问题的一种“多功能工具”。