a committee of 5 people is to be selected from 6 men and 9 w

来源：学生作业帮编辑：作业帮分类：英语作业时间：2024/07/18 06:06:19

a committee of 5 people is to be selected from 6 men and 9 women.If the selection is made randomly,what is the probability that the committee consists of 3 men and 2 women?
翻译：从6男9女中选5个到居委会.如果是随机选择,居委会有3男2女的概率是?
我知道用c6 3*c9 2再÷c15 5只对的.不过我不知道为什么不可以直接用3÷6然后再* 2÷9
求赐教

3÷6然后再* 2÷9 必然不对.这是分批选择的话才是这么做.
比如说吧,你要先在6个人里面选出3个（事件A）,再在9个人里面选2个（事件B）,是可以这么做,因为事件A,B之间是独立的,概率可以直接乘.
但是题目的意思是从15个里面选5,这本身就是单个事件,所以你必须把各种可能的情况都考虑进去.即：恰好选了3女2男的概率 / 所有选择组合的概率,恰好选了3女2男的概率就是C（6,3）*C（9,2）,所有选择组合的概率包含了取的过程中可能出现的0女5男、1女4男、2女3男…的概率（C15 5）.
再问：那为什么不可以把这件事分两步进行首先，在6男中选3（A事件）. 然后再5女中选2（B事件）这两件事不是独立的吗？求赐教
再答：这是题目包含的信息。 a committee of 5 people is to be selected from 6 men and 9 women. 这里的5 people本身就没有性别上的要求，问题中的consists of 3 men and 2 women，只是在这种随机选择情况下所出现的一种结果（If the selection is made randomly）。按照你的说法 (首先，在6男中选3. 然后再5女中选2) ，那就相当于默认了这次选择肯定会选出3男2女。但实际上题目的意思并不是这样的。如果题目这样问，你是不是就会懂了？ Q：从6男9女中选5个到居委会. 如果是随机选择5人，结果可能是5男0女，4男1女，3男2女……现在请问，居委会有3男2女的概率是？

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