题干

2017年,嘉积中学即将迎来100周年校庆.为了了解在校同学们对嘉积中学的看法,学校进行了调查,从三个年级任选三个班,同学们对嘉积中学的看法情况如下:

对嘉积中学的看法

非常好,嘉积中学奠定了

我一生成长的起点

很好,我的中学很快乐很充实

A班人数比例

  

1
2

  

1
2

B班人数比例

  

2
3

  

1
3

C班人数比例

  

3
4

  

1
4

(Ⅰ)从这三个班中各选一个同学,求恰好有2人认为嘉积中学“非常好”的概率(用比例作为相应概率);

(Ⅱ)若在B班按所持态度分层抽样,抽取9人,在这9人中任意选取3人,认为嘉积中学“非常好”的人数记为ξ,求ξ的分布列和数学期望.

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答案(点此获取答案解析)

解:(Ⅰ)记这3位同学恰好有2人认为嘉积中学“非常好”的事件为A,

P(A)=1223

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