鏌愪腑瀛�(xu茅)寰為珮涓�7鍊�(g猫)鐝腑閬稿嚭12鍚嶅(xu茅)鐢熺祫鎴愭牎浠ｈ〃闅�(du矛)锛屽弮鍔犲競涓(xu茅)鏁�(sh霉)瀛�(xu茅)鎳�(y墨ng)鐢ㄩ绔惰辰娲诲嫊(d貌ng)锛屼娇浠ｈ〃涓瘡鐝嚦灏戞湁1浜哄弮鍔犵殑閬告硶鍏辨湁澶氬皯绋紵(462)

銆�鎬濊矾1銆�鍓╀笅鐨�5鍊�(g猫)鍒嗛厤鍒�5鍊�(g猫)鐝礆(j铆).c(5,7)
鍓╀笅鐨�5鍊�(g猫)鍒嗛厤鍒�4鍊�(g猫)鐝礆(j铆).c(1,7)*c(3,6)
鍓╀笅鐨�5鍊�(g猫)鍒嗛厤鍒�3鍊�(g猫)鐝礆(j铆).c(1,7)*c(2,6)+c(2,7)*c(1,5)
鍓╀笅鐨�5鍊�(g猫)鍒嗛厤鍒�2鍊�(g猫)鐝礆(j铆).c(1,7)*c(1,6)+c(1,7)*c(1,6)
鍓╀笅鐨�5鍊�(g猫)鍒嗛厤鍒�1鍊�(g猫)鐝礆(j铆).c(1,7)
鎵€浠�c(5,7)+c(1,7)*c(3,6)+c(1,7)*c(2,6)+c(2,7)*c(1,5)+c(1,7)*c(1,6)+c(1,7)*c(1,6)+c(1,7)=462

銆�鎬濊矾2銆�C(6,11)=462

鍦�10鍊�(g猫)淇＄涓凡鏈�5鍊�(g猫)鏈変俊锛岀敳銆佷箼銆佷笝涓変汉鍚勬嬁涓€灏佷俊锛屼緷娆￠毃渚挎姇鍏ヤ竴淇＄銆傛眰锛�
锛�1锛夌敳銆佷箼鍏╀汉閮芥姇鍏ョ┖淇＄鐨勬鐜囥€�
锛�2锛変笝鎶曞叆绌轰俊绠辩殑姒傜巼銆�

銆�鎬濊矾銆�锛�1锛�A=鐢叉姇鍏ョ┖淇＄锛�B=涔欐姇鍏ョ┖淇＄锛�

P(AB)=C(1,5)*C(1,4)/(10*10)=1/5
锛�2锛�C=涓欐姇鍏ョ┖淇＄锛�

P(C)=P(C*AB)+P(C*  B)+P(C*A )+P(C* )

=(5*4*3+5*5*4+5*6*4+5*5*5)/1000=0.385

瑷�(sh猫)A鏄�3闅庣煩闄ｏ紝b1=(1,2,2)鐨勮綁(zhu菐n)缃櫍锛�b2=(2,-2,1)鐨勮綁(zhu菐n)缃櫍,b3=(-2,-1,2)鐨勮綁(zhu菐n)缃櫍,婊胯冻Ab1=b1,Ab2=2b2,Ab3=3b3,姹�A.

銆�鎬濊矾銆�鍙寲绨＄偤A(b1,b2,b3)'=  (b1,b2,b3)'
姹傚緱A=

宸茬煡P锛�A锛�=X,P(B)=2X,P(C)=3X涓�P(AB)=P(BC),姹�X鐨勬渶澶у€�.

銆�鎬濊矾銆�P(BC)=P(AB)=P(A)=X
P(BC)=P(AB)灏忎簬绛変簬P(A)=X
P(B+C)=P(B)+P(C)-P(BC)澶т簬绛変簬4X
鍙堝洜?y脿n)?/span>P(B+C)灏忎簬绛変簬1
4X灏忎簬绛変簬1     锛�X灏忎簬绛変簬1/4
鎵€浠�X鏈€澶х偤1/4

鍦�1鑷�2000涓毃姗�(j墨)鍙栦竴鍊�(g猫)鏁存暩(sh霉)锛屾眰
锛�1锛夊彇鍒扮殑鏁存暩(sh霉)涓嶈兘琚�6鍜�8鏁撮櫎鐨勬鐜�
锛�2锛夊彇鍒扮殑鏁存暩(sh霉)涓嶈兘琚�6鎴�8鏁撮櫎鐨勬鐜�

銆�鎬濊矾銆�瑷�(sh猫)A=琚�6鏁撮櫎锛�B=琚�8鏁撮櫎;

P(B)=[2000/8]/2000=1/8=0.125锛�

P(A)=[2000/6]/2000=333/2000=0.1665锛�[2000/x]浠ｈ〃2000/x鐨勬暣鏁�(sh霉)閮ㄥ垎锛�
(1)姹�1-P(AB);AB鐐�A 銆�B鐨勬渶灏忓叕鍊嶆暩(sh霉)锛�

P(AB)=[2000/24]/2000=83/2000=0.0415锛涚瓟妗堢偤1-0.0415=0.9585
(2)姹�1-P(A+B);P(A+B)=P(A)+P(B)-P(AB)=0.25;绛旀鐐�1-0.25=0.75.

浠绘剰灏�10鏈浉鏀惧湪鏇告灦涓�锛屽叾涓湁鍏╁鏇�锛屼竴濂�3鍗�锛屼竴濂�4鍗�锛屾眰鍏╁鍚勮嚜鏀惧湪涓€璧�锛岄倓鎸夊嵎娆￠爢鎺掑ソ鐨勬鐜�銆�

銆�鎬濊矾銆�灏囧叐濂楁浉鐪嬩綔鍏╂湰鏇�锛屽姞涓婂彟澶�3鏈�锛屽叡鏈�5鏈紝鏈�5!涓�锛�
鍏╁鏇告瘡涓€濂楁湁鍏╃ó鎺掓硶锛堟寜鍗锋闋嗘帓濂芥湁123鍜�321锛�1234鍜�4321锛�锛�
鎵€浠ョ瓟妗堟槸锛�5锛�*2*2锛�/10锛�

琚嬩腑鏈�20鍊�(g猫)鐞�锛屽叾涓�5鍊�(g猫)绱呯悆锛�15鍊�(g猫)鐧界悆锛屾瘡娆″緸涓彇鍑�5鍊�(g猫)鐞�锛屾渶鍚庝笉鏀惧洖锛屾眰绗笁娆″彇鍑虹殑5鍊�(g猫)鐞冧腑鏈夌磪鐞冪殑姒傜巼銆傦紙绛旀0.628锛�

銆�鎬濊矾銆�瑷�(sh猫)A鐐烘湁绱呯悆锛�Bi鐐哄墠2娆″彇鍑虹磪鐞冩湁i鍊�(g猫)锛�i=0,1,2,...,5锛夊€�(g猫)锛�

鍓囧墿涓�10鍊�(g猫)鐞冧腑鏈夊皪(du矛)鎳�(y墨ng)鏈�5-i鍊�(g猫)绱呯悆銆�
P(Bi)=C(5,i)C(15,10-i)/C(20,10);
P(A/Bi)=1-C(10-(5-i),5)/C(10,5)=1-C(5+i,5)/c(10,5);
P(A)=P锛�A/Bi锛�*P(Bi)涔嬪拰锛�i=0,1,2,...,5锛�

涓€琛ㄩ潰鐐虹磪鑹茬殑姝ｆ柟楂旇鍒嗗壊鎴�1000鍊�(g猫)鍚屾ǎ澶у皬鐨勬鏂归珨锛岀従(xi脿n)鍦ㄥ緸涓换鎰忓彇涓€鍊�(g猫)灏忔鏂归珨锛屾眰鎭版湁鍏╅潰娑傛湁绱呰壊鐨勬鐜�銆�

銆�鎬濊矾銆�姝ｆ柟楂旀湁12姊濇１锛屾瘡姊濇１涓婃湁8鍊�(g猫)绗﹀悎瑕佹眰锛涘叾瀹冨墖涓嶅悎瑕佹眰銆�
绛旀鐐�12*8/1000=0.096

寰�n闆欏瀷铏�(h脿o)鍚勪笉鐩稿悓鐨勯瀷瀛愪腑浠诲彇2r鍙�(2r灏忎簬绛変簬n)锛屾眰涓嬪垪浜嬩欢姒傜巼
锛�1锛�A=娌掓湁涓€闆欓厤灏�(du矛)
锛�2锛�B=鎭版湁涓€闆欓厤灏�(du矛)

銆�鎬濊矾銆�锛�1锛夊厛寰�N闆欓瀷瀛愪腑鍙�2r闆�锛屽湪寰�2r闆欎腑姣忛洐閬�1鍙�銆�