在圆周上依次有
个点
,今随机地选取其中
个点为顶点作凸
边形
,已知选取与否的可能性是相同的,试求对每个
,
边形的两个相邻顶点
(规定
)之间至少有
中的
个点的概率,其中,
是给定的一组正整数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73eb3926f6daed59df80e7914c28b768.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f86ff702f60daaf4aff31db11ed98939.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58c01a2ab8267152b0c3e6e53efe2903.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24220f7001c1fa17f4449a2762fe748d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4de6bcd1060b575b8a77ad33f96738c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6acb05137c136ad72f1f11851bc7f413.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e5c11902ea84677a5981738f096869c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/591ee536bb3d90a3121946520ec34539.png)
2018高三·全国·竞赛 查看更多[1]
更新时间:2018-12-26 23:14:48
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相似题推荐
解答题-问答题
|
较难
(0.4)
【推荐1】对于集合
,若存在两个数列
满足(i)
;(ii)
,则称M为一个“友谊集”,称(A,B)为
的一种“友谊排列”,如A=(3,10,7,9,6)和B=(2,8,4,5,1)便是集合
的一种友谊排列,记为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8814f9d83af2f3976dc98da108f87fae.png)
(1)证明:若
为一个友谊集,则存在偶数种友谊排列;
(2)确定集合
及
的全体友谊排列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31413f381fdeb144d75ffd1a1cd2b72d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70a5369bb892f707c3f0a2ac2fa18f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d51db82726903e34d1eaee5f96f7341.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54946204c502727ffaee3c0172d195a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ddad3d9fdb5e9951b6a1c31f9a72a71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/700537ac93b9dddbeb05d74067a03666.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8814f9d83af2f3976dc98da108f87fae.png)
(1)证明:若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ddad3d9fdb5e9951b6a1c31f9a72a71.png)
(2)确定集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72fa71450b470cb7d6464339873d74b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/700537ac93b9dddbeb05d74067a03666.png)
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解答题-问答题
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较难
(0.4)
【推荐2】设
,(
)是任意的和为正数的
个不同的实数,(
.)是这
个数的一个排列.若对任意的
,有
,则称(
)是一个“好排列”.求好排列个数的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5abda0dafbeb04413299e8bd7be16a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69fd73be954e64b1cdeb7293d4addb94.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a98946ba5ec9894d3645af58f408da0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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解答题-问答题
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较难
(0.4)
【推荐1】已知由1,2,…,1000这1000个正整数构成的集合A,先从集合A中随机取一个数
,取出后把
放回集合A;然后再从集合A中随机取一个数b,求
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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较难
(0.4)
【推荐2】甲和乙轮流掷一枚均匀硬币,谁先掷出正面谁获胜,此时本场结束,而且负方在下一场先掷.
(1)求任一场比赛中,先掷的人获胜的概率;
(2)设他们一共玩了10场,且甲第一场先掷,记甲赢得第k场的概率为
.若
,求k的值.
(1)求任一场比赛中,先掷的人获胜的概率;
(2)设他们一共玩了10场,且甲第一场先掷,记甲赢得第k场的概率为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd33dee1c85ff9faaf1f1a120250674b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b396355233c72d7d0aca542249349f6.png)
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