在现实世界中,一般事件都是相互关联的, 例如你可能是一个早起者, 也有可能是个夜猫子, 例如假如早起者和夜猫子的概率均为0.5, 那么你决定是否明早五点起床去跑步就不是一个独立事件. 如果你是一个早起者, 那么去跑步的概率0.02, 但如果你是一个夜猫子那么概率很可能是0, 你可以把这个过程当作投掷两次硬币, 第一枚硬币决定你是不是早起者, 在你是早起者的情况下,才会投掷第二次硬币. 因此二者不再是相互独立的事件.
条件概率
在这节课中你学习到了条件概率。通常事件并不像掷硬币和骰子一样是独立的。实际上，某个事件的结果依赖于之前的事件。
例如，得到阳性检验测试结果的概率依赖于你是否具有某种特殊条件。如果具备条件，测试结果就是阳性的。我们通过以下方式用公式表示任意两个事件的条件概率：
在这个例子中，我们得到下列内容：
其中 | 代表 "鉴于"，∩ 代表 "和".
- P(A) means "the probability of A"
- P(\neg A)P(¬A) means "the probability of NOT A"
- P(A,B)P(A,B) means "the probability of A and B" and
- P(A|B)P(A∣B) means "the probability of A given B.
习题 1/5
If A and B are independent events and P(A) = 0.2 and P(B) = 0.1, what is P(A,B)?
0.02
习题 2/5
If A and B are NOT independent events, and P(A) = 0.2 and P(B) = 0.1, what is P(A, B)?
信息不足
习题 3/5
If A and B are NOT independent events, and P(A) = 0.2, P(B) = 0.1, and P(B|A) = 0.3 what is P(A|B)?
0.6
Note:
The remaining questions deal with two coins.
Coin 1 is fair. When flipped it has a probability of 0.5 for heads and 0.5 for tails.
Coin 2 is biased. When flipped it has a probability of 0.9 for heads and 0.1 for tails.
习题 4/5
You grab one of these two coins at random (equally likely that you grabbed coin 1 or 2) and you flip it. What's the probability it comes up heads?
0.7
习题 5/5
You grab a coin at random and flip it twice.
What's the probability that it comes up tails both times
0.13
