题干

某高校文学院和理学院的学生组队参加大学生电视辩论赛,文学院推荐了2名男生,3名女生,理学院推荐了4名男生,3名女生,文学院和理学院所推荐的学生一起参加集训,由于集训后学生水平相当,从参加集训的男生中随机抽取3人,女生中随机抽取3人组成代表队.

(1)求文学院至少有一名学生入选代表队的概率;

(2)某场比赛前,从代表队的6名学生在随机抽取4名参赛,记X表示参赛的男生人数,求X的分布列与数学期望.

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答案(点此获取答案解析)

解:(1)由题意,参加集训的男、女学生共有6人,参赛学生全从理学院中抽出(等价于文学院中没有学生入选代表队)的概率为:c33c43

同类题5

阅读下面短文,按要求完成各项任务。

    I went through some difficult times, dealing with the pressures of growing up. I found it hard to communicate with my mother. Relations between us became difficult.

    One day, I ran away from home and stayed away for many hours. When I returned home at night, I saw all the pain, anger and disappointment on my mother’s face. ①      . We agreed to have breakfast together the next morning. It was a turning point in both of our lives and our relationship.

We decided to go to a restaurant. On our way to the table I noticed my mother had two notebooks. I asked her what they were for. She explained to me that sometimes it was easier to write down our feelings rather than talk about (A) them. We would write down our feelings in the form of a letter. It could be as long or as short as we wanted.

    Our first topic was “Why I'm so angry?” I wrote a half page, and my mom filled up nearly three pages. (B) I watched tears run down her face as she wrote. I never realized anyone could hide so much anger. After we finished writing, we exchanged our notebooks. As soon as I started reading my mother's words, I began to cry and so did she. When we finished reading, we discussed our feelings. ②      . Our talk helped me realize so many things I had never thought of before, not only about my mother but also about other people.

     My mother and I continue to use our notebooks as a way of communicating our anger and worries, and our happiness as well. We know that no matter how we feel about each other, our notebooks are a safe place to express our feelings. We have come to an agreement that at the end of each letter we write, “I love you.”