Question

7£®¼Ò²Ï²ÏÌåÓаßÎÆÓɳ£È¾É«ÌåÉϵĻùÒòA¿ØÖÆ£¬»ùÒòÐÍaa±íÏÖΪÎÞ°ßÎÆ£®°ßÎÆÑÕÉ«Óɳ£È¾É«ÌåÉÏÁíÒ»¶Ô»ùÒò£¨B/b£©¿ØÖÆ£¬BB»òBbΪºÚÉ«£¬bbΪ»ÒÉ«£®
£¨1£©ÏÖÑ¡ÓÃÁ½´¿ºÏÇ×±¾¼×¡¢ÒÒÔÓ½»µÃµ½F₁£¬F₁²â½»½á¹ûÈç±í£º

ÐÔ×´	ºÚÉ«°ßÎÆ	»ÒÉ«°ßÎÆ	ÎÞ°ßÎÆ
ÊýÄ¿	91	85	173

Ç×±¾¼×ÐÔ״ΪÎÞ°ßÎÆ£¬ÒҵĻùÒòÐÍΪAABB»òAAbb£®
£¨2£©F₁´ÆÐÛ½»ÅäËùµÃF₂µÄÐÔ×´ºÍ·ÖÀë±ÈΪºÚÉ«°ßÎÆ£º»ÒÉ«°ßÎÆ£ºÎÞ°ßÎÆ=9£º3£º4£® F₂ÖÐ×Ô½»²»·¢ÉúÐÔ×´·ÖÀëµÄ¸öÌåÕ¼$\frac{3}{8}$£®
£¨3£©A/aËùÔÚȾɫÌåż¼ûȱʧÏÖÏó£¬ÈçͼËùʾ£®È¾É«ÌåȱʧµÄÂÑϸ°û²»Óý£¬È¾É«ÌåȱʧµÄ¾«×Ó¿ÉÓý£®»ùÒòÐÍΪA⁰aµÄ²Ï´ÆÐÛ½»Å䣬×Ó´úµÄ±íÏÖÐͺͱÈÀýÓаßÎÆ£ºÎÞ°ßÎÆ=1£º1£®
£¨4£©¼Ò²ÏÖУ¬´ÆÐÔÐÔȾɫÌåΪZW£¬ÐÛÐÔÐÔȾɫÌåΪZZ£®¼Ò²ÏÌå±ÚÕý³£»ùÒò£¨T£©ÓëÌå±Ú͸Ã÷»ùÒò£¨t£©ÊÇλÓÚZȾɫÌåÉϵÄÒ»¶ÔµÈλ»ùÒò£®ÏÖÓÃÓаßÎÆÌå±Ú͸Ã÷´Æ²Ï£¨A⁰aZ^tW£©ÓëÓаßÎÆÌå±ÚÕý³£Ð۲ϣ¨A⁰aZ^TZ^T£©ÔÓ½»µÃµ½F₁£¬½«ÆäÖÐÓаßÎƸöÌåÏ໥½»Å䣬ºó´úÖÐÓаßÎÆÌå±ÚÕý³£ÐÛÐÔ¸öÌåºÍÓаßÎÆÌå±ÚÕý³£´ÆÐÔ¸öÌå·Ö±ðÕ¼$\frac{1}{4}$¡¢$\frac{1}{8}$£®

Answer 1

·ÖÎö ¸ù¾ÝÌâÒâºÍͼ±í·ÖÎö¿ÉÖª£º¼Ò²Ï²ÏÌåÓаßÎÆÓëÎÞ°ßÎÆ¡¢ºÚÉ«Óë»ÒÉ«µÄÒÅ´«×ñÑ­»ùÒòµÄ×ÔÓÉ×éºÏ¶¨ÂÉ£®ÓÉÓÚÖ»ÓÐÓаßÎÆʱ²Å·ÖΪºÚÉ«ºÍ»ÒÉ«£¬ËùÒÔºÚÉ«°ßÎƵĻùÒòÐÍΪA_-B_-£¬»ÒÉ«°ßÎƵĻùÒòÐÍΪA_-bb£¬ÎÞ°ßÎƵĻùÒòÐÍΪaaB_-ºÍaabb£®Ã÷ȷ֪ʶµã£¬ÊáÀíÏà¹ØµÄ»ù´¡ÖªÊ¶£¬·ÖÎöͼ±í£¬½áºÏÎÊÌâµÄ¾ßÌåÌáʾ×ÛºÏ×÷´ð£®

½â´ð ½â£º£¨1£©ÓÉÓÚF₁²â½»½á¹ûΪºÚÉ«°ßÎÆ£º»ÒÉ«°ßÎÆ£ºÎÞ°ßÎÆ=1£º1£º2£¬ËùÒÔF₁µÄ»ùÒòÐÍΪAaBb£®ÓÉÓÚÇ×±¾¼×ÐÔ״ΪÎÞ°ßÎƵĴ¿ºÏÌ壬ËùÒÔÆä»ùÒòÐÍΪaaBB»òaabb£¬Òò´ËÒҵĻùÒòÐÍΪAAbb»òAABB£®
£¨2£©F₁´ÆÐÛ½»ÅäËùµÃF₂µÄÐÔ×´ºÍ·ÖÀë±ÈΪºÚÉ«°ßÎÆ£¨A_-B_-£©£º»ÒÉ«°ßÎÆ£¨A_-bb£©£ºÎÞ°ßÎÆ£¨aaB_-ºÍaabb£©=9£º3£º4£®F₂ÖÐ×Ô½»²»·¢ÉúÐÔ×´·ÖÀëµÄ¸öÌåÕ¼$\frac{1}{16}$+$\frac{1}{16}$+$\frac{4}{16}$=$\frac{3}{8}$£®
£¨3£©ÓÉÓÚȾɫÌåȱʧµÄÂÑϸ°û²»Óý£¬È¾É«ÌåȱʧµÄ¾«×Ó¿ÉÓý£®ËùÒÔ»ùÒòÐÍΪA⁰aµÄ²ÏÖУ¬´ÆÐÔ¸öÌåÖ»ÄܲúÉúaÒ»ÖÖÂÑϸ°û£¬¶øÐÛÐÔ¸öÌåÄܲúÉú2ÖÖ¾«×Ó£¬±ÈÀýΪ1£º1£®Òò´Ë×Ó´úµÄ±íÏÖÐͺͱÈÀýΪÓаßÎÆ£ºÎÞ°ßÎÆ=1£º1£®
£¨4£©ÓаßÎÆÌå±Ú͸Ã÷´Æ²Ï£¨A⁰aZ^tW£©²úÉúµÄÂÑϸ°ûΪaZ^tºÍaW£¬ÓаßÎÆÌå±ÚÕý³£Ð۲ϣ¨A⁰aZ^TZ^T£©²úÉúµÄ¾«×ÓΪA⁰Z^TºÍaZ^T£®ÔòÔÓ½»ËùµÃF₁ÖÐÓаßÎƸöÌåµÄ»ùÒòÐÍΪA⁰aZ^TZ^tºÍA⁰aZ^TW£®Òò´Ë£¬ÓаßÎƸöÌåÏ໥½»Å䣬ºó´úÖÐÓаßÎÆÌå±ÚÕý³£ÐÛÐÔ¸öÌ壨A⁰aZ^TZ^T¡¢A⁰aZ^TZ^t£©Õ¼$\frac{1}{4}$¡Á$\frac{1}{2}$+$\frac{1}{4}$¡Á$\frac{1}{2}$=$\frac{1}{4}$£»ÓаßÎÆÌå±ÚÕý³£´ÆÐÔ¸öÌ壨A⁰aZ^TW£©Õ¼$\frac{1}{4}$¡Á$\frac{1}{2}$=$\frac{1}{8}$£®
¹Ê´ð°¸Îª£º
£¨1£©AABB»òAAbb
£¨2£©ºÚÉ«°ßÎÆ£º»ÒÉ«°ßÎÆ£ºÎÞ°ßÎÆ=9£º3£º4           $\frac{3}{8}$
£¨3£©ÓаßÎÆ£ºÎÞ°ßÎÆ=1£º1
£¨4£©$\frac{1}{4}$        $\frac{1}{8}$

µãÆÀ ±¾Ì⿼²é»ùÒò×ÔÓÉ×éºÏ¶¨ÂɵÄÏà¹Ø֪ʶ£¬ÒâÔÚ¿¼²éѧÉúµÄʶ¼ÇÄÜÁ¦ºÍÅжÏÄÜÁ¦£¬ÔËÓÃËùѧ֪ʶ×ۺϷÖÎöÎÊÌâµÄÄÜÁ¦£®