浙江省高三理科數學一輪復習考試試題精選（1）分類匯編14：概率 Word版含答案

1、浙江省2014屆高三理科數學一輪復習考試試題精選（1）分類匯編14：概率一、填空題 （浙江省溫州中學2014屆高三10月月考數學（理）試題）有一種游戲規(guī)則如下:口袋里有5個紅球和5個黃球,一次摸出5個,若顏色相同則得100分,若4個球顏色相同,另一個不同,則得50分,其他情況不得分,小張摸一次得分的期望是_分. 【答案】 二、解答題 （浙江省溫州市十校聯(lián)合體2014屆高三上學期期初聯(lián)考數學（理）試題）某種項目的射擊比賽,開始時在距目標100m處射擊,如果命中記3分,且停止射擊;若第一次射擊未命中,可以進行第二次射擊,但目標已在150m處,這時命中記2分,且停止射擊;若第二次仍未命中,還可以進行

2、第三次射擊,此時目標已在200m處,若第三次命中則記1分,并停止射擊;若三次都未命中,則記0分,且比賽結束.已知射手甲在100m處擊中目標的概率為,他的命中率與目標的距離的平方成反比,且各次射擊都是獨立的.(1)求射手甲在這次射擊比賽中命中目標的概率;(2)求射手甲在這次射擊比賽中得分的數學期望.【答案】解:記第一、二、三次射擊命中目標分別為事件,三次都未擊中目標為事件d,依題意,設在m處擊中目標的概率為,則,且, ,即, , 由于各次射擊都是相互獨立的, 該射手在三次射擊中擊中目標的概率 （浙江省溫州市十校聯(lián)合體2014屆高三10月階段性測試數學（理）試題）在進行一項擲骰子放球游戲中,規(guī)定:

3、若擲出1點,甲盒中放一球;若擲出2點或3點,乙盒中放一球;若擲出4點或5點或6點,丙盒中放一球,前后共擲3次,設分別表示甲,乙,丙3個盒中的球數.(1)求依次成公差大于0的等差數列的概率;(2)記,求隨機變量的概率分布列和數學期望. 【答案】解:(1)x,y,z依次成公差大于0的等差數列的概率, 即甲、乙、丙3個盒中的球數分別為0,1,2,- 此時的概率- (2)(2)的取值范圍0,1,2,3, 且; ; ; 隨機變量的概率分布列0123p數學期望為- （浙江省溫州市2014屆高三上學期八校聯(lián)考數學（理）試題）一個袋子里裝有7個球, 其中有紅球4個, 編號分別為1,2,3,4;白球3個, 編號

4、分別為2,3,4. 從袋子中任取4個球 (假設取到任何一個球的可能性相同). () 求取出的4個球中, 含有編號為3的球的概率; () 在取出的4個球中, 紅球編號的最大值設為x ,求隨機變量x的分布列和數學期望.【答案】解: () 設“取出的4個球中,含有編號為3的球”為事件a,則 所以,取出的4個球中,含有編號為3的球的概率為 ()隨機變量x的所有可能取值為1,2,3,4 , , , , 所以隨機變量x的分布列是x1234p隨機變量x的數學期望 （浙江省紹興市第一中學2014屆高三上學期回頭考數學（理）試題 ）(本題滿分14分)在兩個不同的口袋中,各裝有大小、形狀完全相同的1個紅球、2個黃

5、球.現(xiàn)分別從每一個口袋中各任取2個球,設隨機變量為取得紅球的個數. ()求的分布列; ()求的數學期望.【答案】解:()由題意的取值為0,1,2. 則; ; ; 所以的分布列為012p ()的數學期望:. 【編號】378 【難度】一般 （浙江省嘉興一中2014屆高三上學期期中數學理試卷）某單位的聯(lián)歡活動中有一種摸球游戲,已知甲口袋中大小相同的3個球,其中2個紅球,1個黑球;乙口袋中有大小相同的2個球,其中1個紅球,1個白球.每次從一只口袋中摸一個球,確定顏色后再放回.摸球的規(guī)則是:先從甲口袋中摸一個球,如果摸到的不是紅球,繼續(xù)從甲口袋中摸一個球,只有當從甲口袋中摸到紅球時,才可繼續(xù)從乙口袋里摸

6、球.從每個口袋里摸球時,如果連續(xù)兩次從同一口袋中摸到的都不是紅球,則該游戲者的游戲停止.游戲規(guī)定,如果游戲者摸到2個紅球,那么游戲者就中獎.現(xiàn)假設各次摸球均互不影響.(i)一個游戲者只摸2次就中獎的概率;(ii)在游戲中,如果某一個游戲者不放棄所有的摸球機會,記他摸球的次數為,求的數學期望.【答案】解:從甲口袋中摸一個球,摸到的球是紅色球的概率為;從乙口袋中摸一個球,摸到的球是紅色球的概率為. (1)一個游戲者只摸2次就中獎,說明他第一次從甲口袋摸到的是紅球,第二次從乙口袋中摸到的也是紅球,所以其概率為; (2)可取.用表示“從甲口袋中摸1個球,摸到的是紅球”,用表示“從甲口袋中摸1個球,摸到

7、的不是紅球”,則;用表示“從乙口袋中摸1個球,摸到的是紅球”,用表示“從乙口袋中摸1個球,摸到的不是紅球”,則. ; ; .234所以的分布列為: . （浙江省嘉興市2014屆高三9月月考數學理試題）一個袋子中裝有6個紅球和4個白球,假設每一個球被摸到的可能性是相等的.(i)從袋子中摸出3個球,求摸出的球為2個紅球和1個白球的概率;(ii)從袋子中摸出2個球,其中白球的個數為,求的分布列和數學期望.【答案】 qcwa3ptgz7r4i30ka1dkaghn3xtkknbycudxqa7fhyi2chhi92tgkqcwa3ptgshls50clmtwn60eo8wgqv7xav2ohum32w

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