Question

6£®ÈçͼÊÇij¼Ò×åÒÅ´«ÏµÆ×ͼ£®¼ÙÉè¼×²¡ÊܵÈλ»ùÒòAºÍa¿ØÖÆ£¬ÒÒ²¡ÊܵÈλ»ùÒòBºÍb¿ØÖÆ£®ÒÑÖª¢ñ-1ÌåÄÚ²»º¬ÒÒ²¡µÄÖ²¡»ùÒò£®Çë»Ø´ð£º

£¨1£©¿ØÖƼײ¡µÄ»ùÒòλÓÚ³£È¾É«ÌåÉÏ£¬ÊôÓÚÒþ£¨Ìî¡°ÏÔ¡±»ò¡°Òþ¡±£©ÐÔ»ùÒò£»¿ØÖÆÒÒ²¡µÄ»ùÒòλÓÚXȾɫÌåÉÏ£¬ÊôÓÚÒþÐÔ»ùÒò£®
£¨2£©¢ñ₁ÄܲúÉú4ÖÖ¾«×Ó£¬¢ò₆µÄ»ùÒòÐÍÊÇAaX^bY»òAAX^bY£®
£¨3£©´ÓÀíÂÛÉÏ·ÖÎö£¬Èô¢ñ₁ºÍ¢ñ₂ÔÙÉúÅ®º¢£¬¿ÉÄÜÓÐ6ÖÖ»ùÒòÐÍ£®
£¨4£©¢ò₇ºÍ¢ò₈ÉúÒ»¸öͬʱ»¼Á½ÖÖ²¡º¢×ӵĸÅÂÊΪ$\frac{1}{24}$£»Èô¢ò₇ºÍ¢ò₈ÒѾ­ÉúÏÂÒ»¸öͬʱ»¼Á½ÖÖ²¡µÄº¢×Ó£¬ÄÇôËûÃÇÔÙÉúÒ»¸öÕý³£Äк¢µÄ¸ÅÂÊΪ$\frac{1}{4}$£®

Answer 1

·ÖÎö ±¾ÌâÖ÷Òª¿¼²éµÄµ¥»ùÒòÒÅ´«²¡¼°×ÔÓÉ×éºÏ¶¨ÂÉ£®ÓÉλÓÚ·ÇͬԴȾɫÌåÉϵÄÁ½¶ÔµÈλ»ùÒòÒýÆðµÄÁ½ÖÖÒÅ´«²¡£¬ËüÃǵÄÒÅ´«¼È·ûºÏ×ÔÓÉ×éºÏ¶¨ÂÉÒ²·ûºÏ°éÐÔÒÅ´«£®¼Ò×åÒÅ´«ÏµÆ×ͼ¿ÉÖª¢ñ₁ºÍ¢ñ₂ ÎÞ²¡ÉúÁËÒ»¸öÓмײ¡µÄÅ®¶ùºÍÒÒ²¡µÄ¶ù×Ó£¬¡°ÎÞÖÐÉúÓÐÊÇÒþÐÔ£¬ÒþÐÔÒÅ´«¿´Å®²¡£¬Å®²¡ÄÐÕý·Ç°éÐÔ¡±£¬ËùÒԼס¢ÒÒ²¡¾ùΪÒþÐÔ£¬¼×²¡Îª³£È¾É«ÌåÒþÐÔÒÅ´«²¡£¬ÓÖÒÑÖª¢ñ-1ÌåÄÚ²»º¬ÒÒ²¡µÄÖ²¡»ùÒò£¬Òò´ËÒÒ²¡Îª°éXÒþÐÔÒÅ´«²¡£®

½â´ð ½â£º£¨1£©ÓÉÒÔÉÏ·ÖÎö¿ÉÖª£º¼×²¡³£È¾É«ÌåÒþÐÔÒÅ´«²¡£¬ÒÒ²¡Îª°éXÒþÐÔÒÅ´«²¡£®
£¨2£©6ºÅ»ùÒòÐÍÊÇA_X^bY£¬¼´Aa^_XbY»òAAX^bY£»¸ù¾Ý6ºÅ£¨A_X^bY£©ºÍ7ºÅ£¨aaX^BX^_£©¿ÉÖª1ºÅµÄ»ùÒòÐÍΪAaX^BY£¬¿É²úÉú4ÖÖ¾«×Ó£®
£¨3£©1ºÅµÄ»ùÒòÐÍΪAaX^BY£¬2ºÅµÄ»ùÒòÐÍΪAaX^BX^b£¬Èô¢ñ1ºÍ¢ñ2ÔÙÉúÅ®º¢¿ÉÄÜÓÐ3¡Á2=6ÖÖ»ùÒòÐÍ£®  
£¨4£©ÓÉÓÚ7ºÅΪaa$\frac{1}{2}$X^BX^b£¬8ºÅΪ$\frac{2}{3}$AaX^BY£¬ËûÃÇÉúÒ»¸öͬʱ»¼Á½ÖÖ²¡º¢×ӵĸÅÂÊΪ£¨1¡Á$\frac{2}{3}¡Á\frac{1}{2}$£©aa¡Á£¨$\frac{1}{2}¡Á\frac{1}{2}¡Á\frac{1}{2}$£©X^bY=$\frac{1}{24}$£¬Õý³£Äк¢µÄ¸ÅÂÊΪ£¨1-$\frac{1}{3}aa$£©¡Á£¨$\frac{1}{2}-\frac{1}{8}$X^bY£©=$\frac{1}{4}$£®
¹Ê´ð°¸Îª£º
£¨1£©³££»Òþ£»X£»Òþ£®
£¨2£©4£»AaX^bY»òAAX^bY   
£¨3£©6
£¨4£©$\frac{1}{24}$£»  $\frac{1}{4}$

µãÆÀ ±¾Ì⿼²éÈËÀàÒÅ´«²¡Óë×ÔÓÉ×éºÏ¶¨ÂÉÏà¹Ø֪ʶ£¬Êì¼Ç¸÷ÖÖÒÅ´«²¡µÄÌص㣬´Ó¶øÅжÏÒÅ´«²¡µÄÒÅ´«·½Ê½ºÍ¸÷¸öÌåµÄ»ùÒòÐÍ£¬ÒªÇó¿¼ÉúÁé»îÓ¦ÓÃ×ÔÓÉ×éºÏ¶¨ÂÉÀ´½â¾ö·ÇͬԴȾɫÌåÉϵÄÁ½¶ÔµÈλ»ùÒòÒýÆðµÄÁ½ÖÖÒÅ´«²¡·¢ÉúµÄ¸ÅÂÊ£¬ÒâÔÚ¿¼²é¿¼ÉúµÄ·ÖÎöÅжϺÍÀí½â¼ÆËãÄÜÁ¦£®