Question

6£®¹ûÓ¬ÖУ¬ºìÑÛ»ùÒò£¨A£©Óë°×ÑÛ»ùÒò£¨a£©Î»ÓÚXȾɫÌåÉÏ£¬³¤³á»ùÒò£¨B£©Óë²Ð³á»ùÒò£¨b£©Î»ÓÚ³£È¾É«ÌåÉÏ£®ÏÖÓÃÁ½¸öºìÑÛ³¤³áµÄ´Æ¡¢ÐÛ¹ûÓ¬Ï໥½»Å䣬ºó´ú±íÏÖÐͼ°±ÈÀýÈç±í£®Çë·ÖÎö»Ø´ð£º

±íÏÖÐÍ	ºìÑÛ³¤³á	ºìÑ۲гá	°×ÑÛ³¤³á	°×Ñ۲гá
´ÆÓ¬	3	1	0	0
ÐÛÓ¬	3	1	3	1

£¨1£©Ç×±¾ÖдÆÐÛ¹ûÓ¬µÄ»ùÒòÐÍ·Ö±ðÊÇBbX^AX^a¡¢BbX^AY£®
£¨2£©´ÆÐÔÇ×±¾²úÉúµÄÕý³£ÂÑϸ°ûÖУ¬ÓëA»ùÒò×éºÏµÄ»ùÒòÊÇB»òb£»°×ÑÛÐÔ×´ÒÅ´«·½Ê½µÄÌصã¸ô´ú½»²æÒÅ´«£®
£¨3£©ÈôÓÃÐÛÐÔÇ×±¾²â½»£¬Ôòºó´úÖÐÓë²â½»µÄÁíÒ»Ç×±¾»ùÒòÐÍÏàͬµÄ¸öÌåÕ¼ºó´ú×ÜÊýµÄ±ÈÀýΪ0£®
£¨4£©ÈôÈÃ×Ó´úÖеĺìÑÛ³¤³á¹ûÓ¬×ÔÓɽ»Å䣬Ôòºó´úÖеij¤³á£º²Ð³áΪ8£º1£¬ºìÑ۵ıÈÀýΪ$\frac{7}{8}$£®

Answer 1

·ÖÎö ¸ù¾ÝÌâÒâºÍͼ±í·ÖÎö¿ÉÖª£ººìÑÛ£¨A£©¶Ô°×ÑÛ£¨a£©ÎªÏÔÐÔ£¬Î»ÓÚXȾɫÌåÉÏ£¬ÊôÓÚ°éÐÔÒÅ´«£»³¤³á£¨B£©¶Ô²Ð³á£¨b£©ÎªÏÔÐÔ£¬Î»ÓÚ³£È¾É«ÌåÉÏ£»ÓëÑÛÉ«»ùÒò·Ö±ðλÓÚÁ½¶ÔͬԴȾɫÌåÉÏ£¬×ñÑ­»ùÒòµÄ×ÔÓÉ×éºÏ¶¨ÂÉ£®ºìÑÛ³¤³áµÄ´Æ¹ûÓ¬£¨B_X^AX-£©ÓëºìÑÛ³¤³áµÄÐÛ¹ûÓ¬£¨B_X^AY£©½»Å䣬ºó´úÐÛ¹ûÓ¬Öг¤³á£º²Ð³á=3£º1£¬Òò´ËÈ·¶¨Ç×±¾¾ùΪÔÓºÏ×Ó£¨Bb¡ÁBb£©£»ÓÖÒòΪÐÛ¹ûÓ¬ÖкìÑÛ£º°×ÑÛ=1£º1£¬ÓÉ´ËÈ·¶¨Ä¸±¾»ùÒòÐÍΪX^AX^a£¬ÔÙÀûÓûùÒòµÄ×ÔÓÉ×éºÏ¶¨ÂɽøÐÐÏà¹Ø¼ÆË㣮

½â´ð ½â£º£¨1£©¸ù¾Ý·ÖÎö£¬Ç×±¾µÄ»ùÒòÐÍÊÇBbX^AYºÍBbX^AX^a£®
£¨2£©ÒÑÖªÁ½¶Ô»ùÒòÔÚÁ½¶ÔͬԴȾɫÌåÉÏ£¬·ÇͬԴȾɫÌåÉϵķ¢µÈλ»ùÒò×ñÑ­×ÔÓÉ×éºÏ¶¨ÂÉ£¬ËùÒÔ´ÆÐÔÇ×±¾²úÉúµÄÕý³£ÂÑϸ°ûÖУ¬ÓëA×éºÏµÄ»ùÒòӦΪB¡¢b£®°×ÑÛÊÇ°éXÒþÐÔÒÅ´«£¬¾ßÓиô´ú½»²æÒÅ´«µÄÌص㣮
£¨3£©ÓÉÓÚÐÛÐÔÇ×±¾µÄ»ùÒòÐÍÊÇBbX^AY£¬ÓëbbX^aX^a½øÐв⽻£¬Ôòºó´úÖÐbbX^aX^aµÄ¸öÌåµÄ¸ÅÂÊΪ0£®
£¨4£©ÒÑÖªÇ×±¾µÄ»ùÒòÐÍÊÇBbX^AYºÍBbX^AX^a£¬ºó´úÖеĺìÑÛ³¤³áÐÛ¹ûÓ¬B_X^AYÓëºìÑÛ³¤³á´Æ¹ûÓ¬B_X^AX^A»òB_X^AX^a½»Å䣬ºó´úÖа×Ñ۵ıÈÀýÊÇ$\frac{1}{2}¡Á\frac{1}{4}$=$\frac{1}{8}$£¬ÔòºìÑ۵ıÈÀýÊÇ$\frac{7}{8}$£»²Ð³áµÄ¸ÅÂÊΪ$\frac{2}{3}$¡Á$\frac{2}{3}$¡Á$\frac{1}{4}$=$\frac{1}{9}$£¬Ôò³¤³á£º²Ð³áΪ8£º1£®
¹Ê´ð°¸Îª£º
£¨1£©BbX^AX^a¡¢BbX^AY    
£¨2£©B»òb  ¸ô´ú½»²æÒÅ´«   
£¨3£©0   
£¨4£©8£º1    $\frac{7}{8}$

µãÆÀ ±¾Ì⿼²éÁË»ùÒòµÄ×ÔÓÉ×éºÏ¶¨ÂÉÔÚ°éÐÔÒÅ´«ÖеÄÓ¦ÓÃÒÔ¼°È¾É«Ìå±äÒ죬ÒâÔÚ¿¼²éѧÉú·ÖÎö±í¸ñµÄÄÜÁ¦¡¢´ÓÌâÖлñÈ¡ÓÐЧÐÅÏ¢µÄÄÜÁ¦¡¢ÒÔ¼°ÄÜÓÃÊýѧ·½Ê½×¼È·µØÃèÊöÉúÎïѧ·½ÃæµÄÄÚÈÝ¡¢ÒÔ¼°Êý¾Ý´¦ÀíÄÜÁ¦£®