An individual has 3 different email accounts. Most of her messages, in fact 70%, come into account #1, whereas come into account #2 and the remaining into account #3. Of the messages into account #1, only 1% are spam, whereas the corresponding percentages for accounts #2 and #3 are and , respectively. What is the probability that a randomly selected message is spam?
示例 2.30 一个个体有 3 个不同的电子邮件账户。她的大部分信息，实际上 70%，都进入了账户 1，而 进入账户 2，剩下的 进入账户 3。在账户 1 中的信息，只有 1% 是垃圾邮件，而账户 #2 和 #3 对应的百分比分别是 和 。随机选取一条信息是垃圾邮件的概率是多少？
To answer this question, let’s first establish some notation:
为了回答这个问题，让我们首先建立一些记号：
message is from account for message is spam
信息来自账户 对于 信息是垃圾邮件
Then the given percentages imply that
那么给出的百分比意味着
Now it is simply a matter of substituting into the equation for the law of total probability:
现在只需将值代入总概率定律的方程中：
In the long run, of this individual’s messages will be spam.
从长远来看， 的这个个体的信息将是垃圾邮件。