µÚÒ»ÕÂ_Ëæ»úʼþ¼°Æä¸ÅÂÊϰÌâ ÏÂÔØ±¾ÎÄ

ÄÚÈÝ·¢²¼¸üÐÂʱ¼ä : 2025/7/12 2:28:49ÐÇÆÚÒ» ÏÂÃæÊÇÎÄÕµÄÈ«²¿ÄÚÈÝÇëÈÏÕæÔĶÁ¡£

13¡¢ ÔÚµ¥Î»Ô°ÄÚËæ»úµØÈ¡Ò»µãQ,ÊÔÇóÒÔQΪÖеãµÃÏÒ³¤³¬¹ý1µÃ¸ÅÂÊ¡¢ ½â: ÔÚµ¥Î»Ô°ÄÚÈÎȡһµãQ,²¢¼ÇQµãµÃ×ø±êΪ(x,y),ÓÉÌâÒâµÃÑù±¾¿Õ¼ä ,¼ÇʼþAΪ¡°ÒÔQΪÖÐÐĵÃÏÒ³¤³¬¹ý1¡±,Ôòʼþ ,¼´

Óɼ¸ºÎ¸ÅÂʼÆË㹫ʽµÃ ¡¢

14¡¢ ÉèA,B¾ÍÊÇÁ½Ê¼þÇÒP (A)=0¡¢6,P (B)=0¡¢7¡¢ ÎÊ(1)ÔÚʲôÌõ¼þÏÂP (AB)È¡µ½×î´óÖµ,×î´óÖµ¾ÍÊǶàÉÙ£¿(2)ÔÚʲôÌõ¼þÏÂP (AB)È¡µ½×îСֵ,×îСֵ¾ÍÊǶàÉÙ£¿

½â:ÓÉP (A) = 0¡¢6,P (B) = 0¡¢7¼´ÖªAB¡Ù¦Õ,(·ñÔòAB = ¦ÕÒÀ»¥³âʼþ¼Ó·¨¶¨Àí, P(A¡ÈB)=P (A)+P (B)=0¡¢6+0¡¢7=1¡¢3 >1ÓëP (A¡ÈB)¡Ü1ì¶Ü)¡¢ ´Ó¶øÓɼӷ¨¶¨ÀíµÃ

P (AB)=P (A)+P (B)£­P (A¡ÈB)

(*)

(1)´Ó0¡ÜP(AB)¡ÜP(A)Öª,µ±AB=A,¼´A¡ÉBʱP(AB)È¡µ½×î´óÖµ,×î´óֵΪ P(AB)=P(A)=0¡¢6,

(2)´Ó(*)ʽ֪,µ±A¡ÈB=ʱ,P(AB)È¡×îСֵ,×îСֵΪ P(AB)=0¡¢6+0¡¢7£­1=0¡¢3 ¡¢ 15¡¢ ÉèA,B¾ÍÊÇÁ½Ê¼þ,Ö¤Ã÷:

Ö¤ P£¨AB?AB£©?P£¨AB)?P(AB)?P(ABAB)?P(A?B)?P(B?A) ¡¢

16¡¢ ijÃÅ¿ÎÖ»ÓÐͨ¹ý¿ÚÊÔ¼°±ÊÊÔÁ½ÖÖ¿¼ÊÔ,·½¿É½áÒµ¡¢ ijѧÉúͨ¹ý¿ÚÊÔ¸ÅÂÊΪ80%,ͨ¹ý±ÊÊԵøÅÂÊΪ65%,ÖÁÉÙͨ¹ýÁ½ÕßÖ®Ò»µÃ¸ÅÂÊΪ75%,ÎʸÃѧÉúÕâÃſνáÒµµÃ¿ÉÄÜÐÔÓжà´ó£¿

½â A=¡°Ëýͨ¹ý¿ÚÊÔ¡±,B=¡°Ëýͨ¹ý±ÊÊÔ¡±,Ôò P(A)=0¡¢8, P(B)=0¡¢65, P(A+B)=0¡¢75 P(AB)=P(A)+P(B)?P(A+B)=0¡¢8+0¡¢65?0¡¢75=0¡¢70

¼´¸ÃѧÉúÕâÃſνáÒµµÃ¿ÉÄÜÐÔΪ70%¡¢

17¡¢ ijµØÓмס¢ÒÒ¡¢±ûÈýÖÖ±¨Ö½,¸ÃµØ³ÉÄêÈËÖÐÓÐ20%¶Á¼×±¨,16%¶ÁÒÒ±¨,14%¶Á±û±¨,ÆäÖÐ8%¼æ¶Á¼×ÓëÒÒ±¨,5%¼æ¶Á¼×Óë±û±¨,4%¼æ¶ÁÒÒÓë±û±¨,ÓÖÓÐ2%¼æ¶ÁËùÓб¨Ö½,ÎʳÉÄêÈËÖÁÉÙ¶ÁÒ»ÖÖ±¨Ö½µÃ¸ÅÂÊ¡¢

½â

¡¢

18¡¢ ÒÑÖª,ÇóʼþÈ«²»·¢ÉúµÃ¸ÅÂÊ¡¢

½âP(ABC)?P(A?B?C)?1?P(A?B?C)?31?3 ?1?[P(A)?P(B)?P(C)?P(AB)?P(AC)?P(BC)?P(ABC)]?1??????48?8¡¢

19.ij³§µÃ²úÆ·ÖÐÓÐ4%µÃ·ÏÆ·,ÔÚ100¼þºÏ¸ñÆ·ÔÚÓÐ75¼þÒ»µÈÆ·,ÊÔÇóÔڸòúÆ·ÈÎȡһ¼þµÃ¾ÍÊÇÒ»µÈÆ·µÃ¸ÅÂÊ¡¢ ½â ¡¢

20¡¢ ÔÚ100¸ö´ÎÆ·ÖÐÓÐ10 ¸ö´ÎÆ· ,ÿ´Î´ÓÈÎȡһ¸ö(²»·Å»Ø),ÇóÖ±µ½µÚ4´Î²ÅÈ¡µ½ÕýÆ·µÃ¸ÅÂÊ¡¢

½â =¡°µÚ´ÎÈ¡µ½ÕýÆ·¡± =1,2,3,4¡¢

21¡¢ ijÈËÍü¼ÇÁ˵绰ºÅÂëµÃ×îºóÒ»¸öÊý×Ö,Òò¶øËæ»úµÃ²¦ºÅ,ÇóËý²¦ºÅ²»³¬¹ýÈý´Î¶ø½ÓͨËùÐèµÃµç»°µÃ¸ÅÂʾÍÊǶàÉÙ£¿

¼ÇH±í²¦ºÅ²»³¬¹ýÈý´Î¶øÄܽÓͨ, Ai±íµÚi´Î²¦ºÅÄܽÓͨ¡¢ ×¢Òâ:µÚÒ»´Î²¦ºÅ²»Í¨,µÚ¶þ²¦ºÅ¾Í²»ÔÙ²¦Õâ¸öºÅÂë¡¢

??H?A1?A1A2?A1A2A3¡¡ÈýÖÖÇé¿ö»¥³âP(H)?P(A1)?P(A1)P(A2|A1)?P(A1)P(A2|A1)P(A3|A1A2)

?1919813??????.10109109810P(AB)?P(A)?P(AB)?P(A)P(B) P(B)22¡¢ Èô,ÇÒ,Ö¤Ã÷¡¢

Ö¤ ÒòΪ P(A|B)?P(A), Ôò ¡¢

23¡¢ Ö¤Ã÷ʼþÓ뻥²»ÏàÈÝ,ÇÒ0<<1,Ôò¡£ Ö¤ ¡¢¡£

24¡¢ ÉèÒ»²Ö¿âÖÐÓÐ10ÏäͬÖÖ¹æ¸ñµÃ²úÆ·,ÆäÖÐÓɼס¢ÒÒ¡¢±ûÈý³§Éú²úµÃ·Ö±ðÓÐ5Ïä¡¢3Ïä¡¢2Ïä,Èý³§²úÆ·µÃ·ÏÆ·ÂÊÒÀ´ÎΪ0¡¢1¡¢0¡¢2¡¢0¡¢3,´ÓÕâ10ÏäÖÐÈÎȡһÏä,ÔÙ´ÓÕâÏäÖÐÈÎȡһ¼þ²úÆ·,ÇóÈ¡µÃÕýÆ·µÃ¸ÅÂÊ¡¢

½â Éè=£ûÈ¡µÃµÃ²úƷΪÕýÆ·£ý, ·Ö±ðΪ¼×¡¢ÒÒ¡¢±ûÈý³§µÃ²úÆ·

= ,=,=,, ËùÒÔ 0¡¢83¡¢

25¡¢ ijһ¹¤³§ÓÐÈý¸ö³µ¼äÉú²úͬһÐͺÅÂݶ¤,ÿ¸ö³µ¼äµÃ²úÁ¿·Ö±ðÕ¼¸Ã³§Âݶ¤×ܲúÁ¿µÃ25 %¡¢35 %¡¢40 %,ÿ¸ö³µ¼ä³ÉÆ·ÖÐµÃ´ÎÆ··Ö±ðΪ¸÷³µ¼ä²úÁ¿µÃ5 %¡¢4 %¡¢2 %,Èç¹û´ÓÈ«³§×ܲúÆ·Öгéȡһ¼þ²úÆ·Âݶ¤Îª´ÎÆ·,ÎÊËü¾ÍÊdzµ¼äÉú²úµÃ¸ÅÂÊ¡¢

½â ·Ö±ð±íʾÈý³µ¼äÉú²úµÃÂݶ¤,=¡°±íʾ´ÎÆ·Âݶ¤¡±

== ͬÀí = ; =¡¢

26¡¢ ÒÑÖªÄÐÈËÖÐÓÐ5 %µÃɫ仼Õß,Å®ÈËÖÐÓÐ0¡¢25 %µÃɫ仼Õß,½ñ´ÓÄÐÅ®ÈËÊýÖÐËæ»úµØÌôѡһÈË,Ç¡ºÃ¾ÍÊÇɫ仼Õß,ÎÊ´ËÈ˾ÍÊÇÄÐÐԵøÅÂʾÍÊǶàÉÙ£¿

½â =£û´ÓÈËȺÖÐÈÎȡһÈ˾ÍÊÇÄÐÐÔ£ý, =£ûɫ仼Õߣý

ÒòΪ

P(A)?P(B)P(A|B)?P(B)P(A|B)?0.5?0.05?0.5?0.0025?0.02625 ËùÒÔ ¡¢

27¡¢ÉèA,BÊÇÈÎÒâ¶þʼþ,ÆäÖÐAµÄ¸ÅÂʲ»µÈÓÚ0ºÍ1, Ö¤Ã÷,P(B|A)?P(B|A)¾ÍÊÇʼþ¶ÀÁ¢µÃ³ä·Ö±ØÒªÌõ¼þ¡¢ Ö¤

P(AB)P(AB)?P(A)P(A) ?[1?P(A)]P(AB)?P(A)[P(B)?P(AB)]

P(B|A)?P(B|A)? ?P(AB)?P(A)P(B),¼´AºÍB¶ÀÁ¢.28¡¢ ÉèÁù¸öÏàͬµÃÔª¼þ,ÈçÏÂͼËùʾÄÇÑù °²ÖÃÔÚϵͳÖÐ,Éèÿ¸öÔª¼þÕý³£¹¤×÷µÃ¸ÅÂÊ Îª,ÇóÕâ¸öϵͳÕý³£¹¤×÷µÃ¸ÅÂÊ¡£¼Ù¶¨¸÷¸ö ÄÜ·ñÕý³£¹¤×÷¾ÍÊÇÏ໥¶ÀÁ¢µÃ¡¢ ½â: Éè , ,

ÓÉÌõ¼þÖª,,, ¡¢

[¶þÊ®Áù(1)]ÉèÓÐ4¸ö¶ÀÁ¢¹¤×÷µÃÔª¼þ1,2,3,4¡£ËüÃǵÿɿ¿ÐÔ·Ö±ðΪP1,P2,P3,P4,½«ËüÃǰ´

ͼ(1)µÃ·½Ê½Áª½Ó,ÇóϵͳµÃ¿É¿¿ÐÔ¡£

¼ÇAi±íʾµÚi¸öÔª¼þÕý³£¹¤×÷,i=1,2,3,4,

2 1 4 3 A±íʾϵͳÕý³£¡£

¡ß A=A1A2A3+ A1A4Á½ÖÖÇé¿ö²»»¥³â

(¼Ó·¨¹«Ê½)

¡à P (A)= P (A1A2A3)+P (A1A4)£­P (A1A2A3 A4)

= P (A1) P (A2)P (A3)+ P (A1) P (A4)£­P (A1) P (A2)P (A3)P (A4) = P1P2P3+ P1P4£­P1P2P3P4

(A1, A2, A3, A4¶ÀÁ¢)

29¡¢ ijÀàµçµÆÅÝʹÓÃʱÔÚ1000СʱÒÔÉϵøÅÂÊΪ0¡¢2,ÇóÈý¸öµÆÅÝÔÚʹÓÃ1000СÒÔºó×î¶àÖ»ÓÐÒ»¸ö»µµÃ¸ÅÂÊ¡¢

½â ±íʾһ¸öµÆÅÝʹÓÃʱÊýÔÚ1000СʱÒÔÉÏ

£ûÈýµÆÅÝÖÐ×î¶àÓÐÒ»¸ö»µ£ý=£ûÈý¸öÈ«ºÃ£ý+£ûÖ»ÓÐÒ»¸ö»µ£ý = (0¡¢2)3+(0¡¢2)2(1¨C0¡¢2)=0¡¢104¡¢

30¡¢ Ò»ÉäÊÖ¶ÔͬһĿ±ê¶ÀÁ¢½øÐÐÁËËÄ´ÎÉä»÷,ÈôÖÁÉÙÃüÖÐÒ»´ÎµÃ¸ÅÂÊΪ, Çó¸ÃÉäÊÖµÃÃüÖÐÂÊ¡¢

802?1?½â ?1?P(ÃüÖÐ 0 ´Î£©?1?£¨1?p)4, (1?p)4????p?¡¢

813?3?31¡¢ ijÐͺŵøßÉäÅÚ,ÿÃÅÅÚ·¢ÉäÒ»·¢»÷ÖеøÅÂÊΪ0¡¢6,ÏÖÈô¸ÉÃÅÅÚͬʱ·¢ÉäÒ»·¢,ÎÊÓûÒÔ99%µÃ°ÑÎÕ»÷ÖÐÀ´·¸µÃÒ»¼ÜµÐ»úÖÁÉÙÐèÒªÅäÖü¸ÃÅÅÚ£¿

½â ÉèÐèÒªÅäÖÃßßÉäÅÚ

=¡°¸ßÅÚ»÷Öзɻú¡±, Ôò

£û·É»ú±»»÷ÖУý=£ûßßÉäÅÚÖÐÖÁÉÙÓÐÒ»ÃÅ»÷ÖУý =1¨C£ûßßÉäÅÚÈ«²»ÃüÖУý

ÖÁÉÙÅ䱸6ÃÅÅÚ¡¢

32¡¢ ÉèÓÐÈýÃÅ»ðÅÚͬʱ¶ÔijĿ±êÉä»÷,ÃüÖиÅÂÊ·Ö±ðΪ0¡¢2¡¢0¡¢3¡¢0¡¢5,Ä¿±êÃüÖÐÒ»·¢±»»÷»ÙµÃ¸ÅÂÊΪ0¡¢2,ÃüÖжþ·¢±»»÷»ÙµÃ¸ÅÂÊΪ0¡¢6,Èý·¢¾ùÃüÖб»»÷»ÙµÃ¸ÅÂÊΪ0¡¢9,ÇóÈýÃÅ»ðÅÚÔÚÒ»´ÎÉä»÷Öл÷»ÙÄ¿±êµÃ¸ÅÂÊ¡¢

4 ½â Éè=£ûÄ¿±êÒ»´ÎÉä»÷Öб»»÷»Ù£ý=£ûÄ¿±ê±»»÷Öе÷¢Êý£ý,(0,1,2,3,)

Ôò

=0¡¢2¡Á0¡¢7¡Á0¡¢5+0¡¢8¡Á0¡¢3¡Á0¡¢5+0¡¢8¡Á0¡¢7¡Á0¡¢5=0¡¢47 =0¡¢2¡Á0¡¢3¡Á0¡¢5+0¡¢2¡Á0¡¢7¡Á0¡¢5+0¡¢8¡Á0¡¢3¡Á0¡¢5=0¡¢22 =0¡¢2¡Á0¡¢3¡Á0¡¢5=0¡¢03

ËùÒÔ 0¡¢47¡Á0¡¢2+0¡¢2¡Á0¡¢6+0¡¢03¡Á0¡¢9=0¡¢253¡¢