Question

15£®Ä³´ÆÐÛͬÖêÖ²ÎﻨµÄÑÕÉ«ÓÉÁ½¶Ô»ùÒò£¨AºÍa£¬BºÍb£©¿ØÖÆ£¬A»ùÒò¿ØÖÆÉ«Ëصĺϳɣ¨AAºÍAaµÄЧӦÏàͬ£©£¬BΪÐÞÊλùÒò£¬µ­»¯ÑÕÉ«µÄÉî¶È£¨BBºÍBbµÄЧӦ²»Í¬£©£®Æä»ùÒòÐÍÓë±íÏÖÐ͵ĶÔÓ¦¹Øϵ¼ûÏÂ±í£¬Çë»Ø´ðÏÂÁÐÎÊÌ⣺

»ùÒò×éºÏ	A_Bb	A_bb	A_BB»òaa__
Ö²ÎﻨÑÕÉ«	·ÛÉ«	ºìÉ«	°×É«

£¨1£©´¿ºÏ°×»¨Ö²ÖêºÍ´¿ºÏºì»¨Ö²ÖêÔÓ½»£¬²úÉúµÄ×Ó´úÖ²Ö껨ɫȫΪ·ÛÉ«£®Çëд³ö¿ÉÄܳöÏÖÕâÖÖ½á¹ûµÄÇ×±¾»ùÒòÐÍ·Ö±ðΪAABB¡ÁAAbb»òaaBB¡ÁAAbb£®
£¨2£©ÎªÌ½¾¿Á½¶Ô»ùÒò£¨AºÍa£¬BºÍb£©ÊÇÔÚͬһ¶ÔͬԴȾɫÌåÉÏ£¬»¹ÊÇÔÚÁ½¶ÔͬԴȾɫÌåÉÏ£¬Ä³Ñо¿Ð¡×éÑ¡ÓûùÒòÐÍΪAaBbµÄ·ÛÉ«»¨Ö²Öê½øÐÐ×Ô½»ÊµÑ飮
¢ÙʵÑé¼ÙÉ裺ÕâÁ½¶Ô»ùÒòÔÚȾɫÌåÉϵÄλÖôæÔÚÈýÖÖÀàÐÍ£¬ÇëÄã²¹³ä»­³öϱíÖÐÆäËûÁ½ÖÖÀàÐÍ£¨ÓÃÊúÏß±íʾȾɫÌ壬ºÚµã±íʾ»ùÒòÔÚȾɫÌåÉϵÄλµã£©£®

ÀàÐͱàºÅ	¼×	ÒÒ	±û
»ùÒò·Ö²¼Î»ÖÃ

¢ÚʵÑé·½·¨£º·ÛÉ«Ö²Öê×Ô½»£®
¢ÛʵÑé²½Ö裺
µÚÒ»²½£º¸Ã·ÛÉ«Ö²Öê×Ô½»£®
µÚ¶þ²½£º¹Û²ì²¢Í³¼Æ×Ó´úÖ²Ö껨µÄÑÕÉ«ºÍ±ÈÀý£®
¢ÜʵÑé¿ÉÄܵĽá¹û£¨²»¿¼Âǽ»²æ»¥»»£©¼°ÏàÓ¦µÄ½áÂÛ£º
a£®Èô×Ó´úÖ²ÖêµÄ»¨É«¼°±ÈÀýΪ·ÛÉ«£ººìÉ«£º°×É«=6£º3£º7£¬ÔòÁ½¶Ô»ùÒòÔÚÁ½¶ÔͬԴȾɫÌåÉÏ£¨·ûºÏ¼×ÀàÐÍ£©£»
b£®Èô×Ó´úÖ²ÖêµÄ»¨É«¼°±ÈÀýΪ·ÛÉ«£º°×É«=1£º1£¬ÔòÁ½¶Ô»ùÒòÔÚÒ»¶ÔͬԴȾɫÌåÉÏ£¨·ûºÏÒÒÀàÐÍ£©£»
c£®Èô×Ó´úÖ²ÖêµÄ»¨É«¼°±ÈÀýΪ·ÛÉ«£ººìÉ«£º°×É«=2£º1£º1£¬ÔòÁ½¶Ô»ùÒòÔÚÒ»¶ÔͬԴȾɫÌåÉÏ£¨·ûºÏ±ûÀàÐÍ£©£®

Answer 1

·ÖÎö 1¡¢»ùÒò×ÔÓÉ×éºÏ¶¨ÂɵÄʵÖÊ£º½øÐÐÓÐÐÔÉúÖ³µÄÉúÎïÔÚ½øÐмõÊý·ÖÁѲúÉúÅä×ӵĹý³ÌÖУ¬Î»ÓÚ·ÇͬԴȾɫÌåÉϵķǵÈλ»ùÒòËæ·ÇͬԴȾɫÌåµÄ×ÔÓÉ×éºÏ¶ø·¢Éú×ÔÓÉ×éºÏ£¬ÓÉÓÚ×ÔÓÉ×éºÏ¶¨ÂÉÒ²×ñÑ­·ÖÀ붨ÂÉ£¬Òò´Ë¿ÉÒÔͨ¹ý·ÖÎö·ÖÀ붨Âɽâ¾ö×ÔÓÉ×éºÏÎÊÌ⣮
2¡¢Î»ÓÚÒ»¶ÔͬԴȾɫÌåÉϵķǵÈλ»ùÒò²»×ñÑ­×ÔÓÉ×éºÏ¶¨ÂÉ£¬×ñÑ­Á¬Ëø¶¨ÂÉ£¬½â¾öÁ¬ËøÎÊÌ⣬¿ÉÒÔÏÈ·ÖÎöͬԴȾɫÌåµÄÐÐΪ½ø¶øд³öÅä×ÓµÄÀàÐͼ°±ÈÀý£¬°´ÕÕ´ÆÐÛÅä×ÓËæ»ú½áºÏд³öºó´úµÄ»ùÒòÐÍ£¬½áºÏÌâ¸ÉÐÅÏ¢ÅжϺó´úµÄ±íÏÖÐͼ°±ÈÀý£®
3¡¢Éè¼ÆʵÑéÅжϻùÒòµÄλÖ㬿ÉÒÔÏȼٶ¨Ä³ÖÖλÖùØϵ³ÉÁ¢£¬ÓÃÒÅ´«¹æÂÉд³ö×Ô½»ºó´úµÄ»ùÒòÐÍ£¬½ø¶øÅжϺó´úµÄ±íÏÖÐÍ£¬ÓÃÑÝÒïÍÆÀíµÄ·½·¨½â´ð£®

½â´ð ½â£º£¨1£©ÓÉÌâ¸ÉÐÅÏ¢¿ÉÖª£¬´¿ºÏ°×»¨Ö²ÖêµÄ»ùÒòÐÍÊÇAABB¡¢aaBB¡¢aabb£¬´¿ºÏºì»¨Ö²ÖêµÄ»ùÒòÐÍÊÇAAbb£¬¶þÕßÔÓ½»ºó´úÖ²Ö껨ɫȫΪ·ÛÉ«£¬»ùÒòÐÍÊÇA_Bb£¬Òò´ËÇ×±¾°×»¨ÖÐÒ»¶¨º¬ÓÐBB»ùÒò£¬Ç×±¾°×»¨»ùÒò×é³ÉÊÇAABB»òaaBB£®
£¨2£©ÕâÁ½¶ÔµÈλ»ùÒòÈç¹ûλÓÚÁ½¶ÔͬԴȾɫÌåÉÏ£¬Ôò×ñÑ­×ÔÓÉ×éºÏ¶¨ÂÉ£¬Èç¹ûλÓÚÒ»¶ÔͬԴȾɫÌåÉÏ£¬Ôò²»×ñÑ­×ÔÓÉ×éºÏ¶¨ÂÉ£¬Î»ÓÚÒ»¶ÔͬԴȾɫÌåÉÏ¿ÉÄÜÓÐ2ÖÖÇé¿ö£¬ABÁ¬Ëø¡¢abÁ¬Ëø£¬»òÕßÊÇAbÁ¬Ëø¡¢aBÁ¬Ëø£®
»ùÒòÐÍΪAaBbµÄ¸öÌå×Ô½»£¬»ùÒò²»Í¬Î»Öã¬×Ô½»ºó´úµÄ±íÏÖÐͼ°±ÈÀý²»Í¬£®
a¡¢Èç¹û·Ö±ðλÓÚ2¶ÔͬԴȾɫÌåÉÏ£¬Ôò×ñÑ­×ÔÓÉ×éºÏ¶¨ÂÉ£¬×Ô½»ºó´úA_=$\frac{3}{4}$¡¢aa=$\frac{1}{4}$£¬BB=$\frac{1}{4}$¡¢Bb=$\frac{1}{2}$¡¢bb=$\frac{1}{4}$
×Ô½»ºó´úºìÉ«Ö²ÖêA_bb=$\frac{3}{4}¡Á\frac{1}{4}=\frac{3}{16}$¡¢·ÛÉ«Ö²ÖêA_Bb=$\frac{3}{4}¡Á\frac{1}{2}=\frac{3}{8}$£¬°×É«Ö²ÖêÊÇA_BB+aa_ _=$\frac{3}{4}¡Á\frac{1}{4}+\frac{1}{4}¡Á1$=$\frac{7}{16}$£¬·ÛÉ«£ººìÉ«£º°×É«=6£º3£º7£®
b¡¢Èç¹ûABÁ¬Ëø¡¢abÁ¬Ëø£¬AaBb²úÉúµÄÅä×ÓµÄÀàÐͼ°±ÈÀýÊÇAB£ºab=1£º1£¬×Ô½»ºó´úµÄ»ùÒòÐͼ°±ÈÀýÊÇAABB£ºAaBb£ºaabb=1£º2£º1£¬ÆäÖÐAABB¡¢aabb±íÏÖΪ°×É«£¬AaBb±íÏÖΪ·ÛÉ«£¬·ÛÉ«£º°×É«=1£º1£®
c¡¢Èç¹û·ûºÏ±û£¬¼´AbÁ¬Ëø¡¢aBÁ¬Ëø£¬AaBb²úÉúµÄÅä×ÓµÄÀàÐͼ°±ÈÀýÊÇAb£ºaB=1£º1£¬ÔòAaBb×Ô½»ºó´úµÄ»ùÒòÐͼ°±ÈÀýÊÇAAbb£¨ºìÉ«£©£ºAaBb£¨·ÛÉ«£©£ºaaBB£¨°×É«£©=1£º2£º1£®
¹Ê´ð°¸Îª£º
£¨1£©AABB¡ÁAAbb»òaaBB¡ÁAAbb
£¨2£©¢Ù    
¢Û¹Û²ì²¢Í³¼Æ×Ó´úÖ²Ö껨µÄÑÕÉ«ºÍ±ÈÀý
¢Ü·ÛÉ«£ººìÉ«£º°×É«=6£º3£º7¡¡  Á½¶Ô»ùÒòÔÚÒ»¶ÔͬԴȾɫÌåÉÏ
·ÛÉ«£ººìÉ«£º°×É«=2£º1£º1

µãÆÀ ±¾ÌâÖ¼µÄ֪ʶµãÊÇ»ùÒò×ÔÓÉ×éºÏ¶¨ÂɵÄʵÖÊ£¬¶à»ùÒò¿ØÖÆһЧӦµÄÏÖÏó£¬Ö¼ÔÚ¿¼²éѧÉúÀí½âËùѧ֪ʶµÄÒªµã£¬°ÑÎÕ֪ʶµÄÄÚÔÚÁªÏµ£¬ÐγÉ֪ʶÍøÂ磬²¢Ñ§»áÓ¦ÓÃÑÝÒïÍÆÀíµÄ·½·¨½â´ðÎÊÌ⣮