首先，回顾一下前一课的 Simple Probability

如果我们要找一个event在设定情况下会发生的Probability/概率，可以用一下的formula：
$$P(event) = \frac{no. of (event)}{totalno.in(Sample Space)}$$

在找一个event的probability时，event只是占了sample space的一部分，对吧？那没有被占的部分，就是这一课里会学到的。。。 “complement of an event”。

Complement 的意思是 “补充的” 或 “使完善的” ... make a thing more complete.

所以，complement of an event就是指除了event, 使sample space完整的那个部分。

既然，complement of an event 和 event 是在同一个 sample space里的，那加起就会等于1。

$$P(A) + P(A') = 1$$ $$or$$ $$1 - P(A) = P(A')$$

A' 代表 complement of event A

(Figure 1)

1. Figure 1 shows the cards that are in Alex's hands. In the event of Alex playing all of his spades ♠️ cards. Which of the following set represents the complement of the event in Alex's hands?
   
   A: {5 of spades, 4 of diamonds, 3 of clubs, 2 of hearts, ace of spades}
   B: {4 of diamonds, 3 of clubs, 2 of hearts}
   C: {4 of diamonds, 3 of clubs, 2 of hears, ace of spades}
   

照图里看Alex手上有5张牌。题目说Alex打出所有的黑桃牌，那剩下在Alex手里的牌就不会有黑桃 ♠️ 了。所以，答案是B

2. There 52 playing cards in a deck, and there are 4 ace cards, 12 face cards, the rest is number cards. What is the probability of the complement of getting a face card?

$$\begin{aligned} Probability\ (face\ card) &= \frac{no.\ of\ face\ card}{total\ no.\ of\ cards} \\ &= \frac{12}{52} \end{aligned} $$ $$\begin{aligned} Complement\ of\ (face\ card')&: \\ 1 - \frac{12}{52} &= \frac{52}{52} - \frac{12}{52} \\ &=\frac{40}{52} \\ &=\frac{10}{13} \end{aligned} $$

这个题目里的event，就是扑克牌里的face cards。所以，可以用1减去probability of face cards 就是扑克牌其它部分的概率。