2016年5月7日福州高三质检文科数学含答案
································· 3分 假设H0:喜欢娱乐节目A与观众性别无关，
540
5.934 3.841， ···························· 5分
39 21 30 3091
所以能在犯错误的概率不超过0.05的前提下认为喜欢娱乐节目A与观众性别有关． ·············································································································· 6分
则K的观测值k=
2
60 24 15 15 6
2
（Ⅱ）利用分层抽样在男性观众30名中抽取5名，其中喜欢娱乐节目A的人数为24 不喜欢节目A的人数为6
5
4，30
5
································································· 7分 =1．
30
被抽取的喜欢娱乐节目A的4名分别记为a,b,c,d；不喜欢节目A的1名记为B． 则从5名中任选2人的所有可能的结果为： a,b , a,c , a,d , a,B , b,c , b,d , b,B ,
c,d , c,B , d,B ，共有10种．
·············································································································· 9分 其中恰有1名喜欢节目A和1名不喜欢节目A的有 a,B , b,B , c,B , d,B ，共4种． ············································································································ 10分
42
所以所抽取的观众中恰有1名喜欢节目A和1名不喜欢节目A的观众的概率是：=．
105
············································································································ 12分 （19）本小题主要考查空间直线与直线、直线与平面的位置关系及三棱锥的高等基础知识，考查空间想象能力、推理论证能力、运算求解能力，考查化归与转化思想等．满分12分． （Ⅰ）证明：取AP的中点F，连结DF,EF，如图所示． 因为点E是PB中点，
AB
所以EF//AB且EF ． ······································ 1分
2AB
又因为AB//CD且CD ，
2
所以EF//CD且EF CD， ······································ 2分 所以四边形EFDC为平行四边形， 所以CE//DF， ····················································· 3分 因为AB 平面PAD，DF 平面PAD， 所以AB DF． ··········································
··········· 4分
所以CE AB． ······················································ 5分 （Ⅱ）解：设点O为PD的中点，连结AO，如图所示， 因为EC AB 4，
··········································· 6分 由（Ⅰ）知，DF ·
又因为AB 4，所以PD AD 2，
