题干

某校举行“庆元旦”教工羽毛球单循环比赛(任意两个参赛队只比赛一场),共有高一、高二、高三三个队参赛,高一胜高二的概率为
1
2
,高一胜高三的概率为
2
3
,高二胜高三的概率为P,每场胜负独立,胜者记1分,负者记0分,规定:积分相同者高年级获胜.
(Ⅰ)若高三获得冠军概率为
1
3
,求P.
(Ⅱ)记高三的得分为X,求X的分布列和期望.
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答案(点此获取答案解析)

解:(Ⅰ)高三获得冠军有两种情况,高三胜两场,三个队各胜一场.
高三胜两场的概率为
1
3
×(1p)
三个队各胜一场的概率为

同类题2

阅读下面的文言文,完成小题。
                                                                                                              (一)
        齐有甄彬者,有器业。尝以一束苎,于荆州长沙西库质钱。后赎苎,于束中得金五两,以手巾裹之。彬得金,送还西库。道人大惊曰:“近有人以金质钱,时忽遽,不记录。檀越乃能见归,恐古今未之有也。”辄以金之半仰酬,往复十余,坚然不受。因咏曰:“五月披羊裘负薪,岂拾遗者也?”彬后为郫令,将行,辞太祖。时同列五人,上诫以廉慎。至于彬,独曰:“卿昔有还金之美,故不复以此诫也。”
                                                                                                               (二)
         公孙仪相鲁而嗜鱼,一国尽争买鱼而献之,公仪子不受。其弟子谏曰:“夫子嗜鱼而不受者,何也?”对曰:“夫唯嗜鱼,故不受也。夫即受鱼,必有下人之色;有下人之色,将枉于法;枉于法,则免于相。虽嗜鱼,此不必致我鱼,我又不能自给鱼。即无受鱼而不免于相,虽嗜鱼,我能常自给鱼。”此明夫恃人不如自恃也。
〔注释〕①器业:高尚的品质和出色的才能。②苎zhù:苎麻。③遽:匆忙。④檀越:指“施主”。⑤郫pí:地名,今四川境内。⑥公孙仪:春秋时鲁穆公的相。⑦下人:迁就他人。                   

同类题4

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    To prevent the deserts coming near, China has planted billions of trees—to replace destroyed forests and as barriers against the sand. This isn't a cure, though, say experts, as thirsty trees can make the problem worse by taking in groundwater.

    “Planting tress is one way, but it isn't that simple. It doesn't solve the basic issue of water resources,” says Wu Bo, a professor. “We need to calculate how much water the trees will absorb, or else it could have a negative effect.”

    Villagers in Zhengxin have taken on this challenge, with limited success. When the irrigation channels began to run dry, Lu Xianglin switched from wheat to cotton on his land. He also planted trees to protect his fields from sandstorms. He says he still gets good yields(产量) using flood irrigation and earns a good income for his family.

    Other farmers haven't stuck it out(坚持到底): about one in three have left Zhengxin in the past 10 years after their wheat crops died. Young people who can find jobs in the towns rarely return.

    Last week, Mr Lu joined the other men in his village on a government-arranged trip to see the land that has been set aside for their relocation, nearly 40 miles to the south. The next day, he was back, shaking his head at the plan. The idea of uprooting his family troubles him, as does the idea of giving up the land that fed his forefathers. He prefers to stay and keep up the fight.

    “With enough water, this problem can be solved,” Lu says. “We can plant trees and grass, and they will grow bigger. That will stop the desert.”

    Experts say that farmers could switch to drip irrigation (滴灌)to lessen their water intake for growing crops. Elsewhere in the region, farmers have built brick greenhouses as part of a plan to grow vegetables using less water. Roadside signs urge farmers to “Save Water, Protect the Environment”.