题干

为了解少年儿童的肥胖是否与常喝碳酸饮料有关,现对30名六年级学生进行了问卷调查,得到如下列联表(平均每天喝500ml以上为常喝,体重超过50kg为肥胖):

常喝
不常喝
合计
肥胖

2

不肥胖

18

合计


30
已知在全部30人中随机抽取1人,抽到肥胖的学生的概率为15
4
(Ⅰ)请将上面的列联表补充完整;
(Ⅱ)是否有99.5%的把握认为肥胖与常喝碳酸饮料有关?说明你的理由;
(Ⅲ)现从常喝碳酸饮料且肥胖的学生中(2名女生),抽取2人参加电视节目,则正好抽到一男一女的概率是多少
P(K2≥k)
0.15
0.10
0.05
0.025
0.010
0.005
0.001
K
2.072
2.706
3.841
5.024
6.635
7.879
10.828
(参考公式:K2=
n
a
d
-
b
c
2
a
+
b
c
+
d
a
+
c
b
+
d
,其中n=a+b+c+d)
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答案(点此获取答案解析)

解:(I)设常喝碳酸饮料肥胖的学生有x人,30
x
+
2
=15
4
,x=6.
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