ÌâÄ¿ÄÚÈÝ
4£®ÒÑÖª¾ßÓÐB»ùÒòµÄ¹·£¬Æ¤Ã«¿ÉÒԳʺÚÉ«£¬¾ßÓÐbb»ùÒòµÄ¹·£¬Æ¤Ã«¿ÉÒԳʺÖÉ«£®ÁíÓÐI£¨i£©»ùÒòÓë¹·µÄëɫÐγÉÒ²Óйأ¬µ±I»ùÒò´æÔÚʱ¹·µÄëɫΪ°×룮ÕâÁ½¶Ô»ùÒòλÓÚÁ½¶Ô³£È¾É«ÌåÉÏ£®Èçͼ1ÊÇÓйع·Ã«É«µÄÔÓ½»ÊµÑ飺£¨1£©Èç¹ûÈÃF2ÖкÚë¹·Ëæ»ú½»Å䣬ÀíÂÛÉÏÆäºó´úÖкÖë¹·µÄ¸ÅÂÊÊÇ$\frac{1}{9}$£®Èç¹ûÈÃF2ÖкÖë¹·ÓëF1½»Å䣬ÀíÂÛÉÏÆäºó´úµÄ±íÏÖÐͼ°ÆäÊýÁ¿±ÈӦΪ°×ë¹·£ººÚë¹·£ººÖë¹·=2£º1£º1£®
£¨2£©BÓëb»ùÒò²»Í¬£¬Æä±¾ÖÊÔÒòÊǼî»ù¶ÔµÄÅÅÁÐ˳Ðò²»Í¬£®
£¨3£©Í¼2ΪF1µÄ°×ë¹·µÄij×éÖ¯ÇÐÆ¬ÏÔ΢ͼÏ󣬸ÃͼÏóÀ´×Ô´ÆÐÔÇ×±¾£¬ÒÀ¾ÝÊÇͼÖбêºÅ¢ÚµÄϸ°ûµÄ²»¾ùµÈ·ÖÁÑ£®
£¨4£©Ï¸°û¢ÛÓëϸ°û¢ÙÏà±È½Ï£¬³ýϸ°û´óСÍ⣬×îÃ÷ÏÔµÄÇø±ðÊÇϸ°û¢Û²»º¬ÓÐͬԴȾɫÌ壬ÇÒȾɫÌåÊýÄ¿¼õ°ë£®
·ÖÎö ·ÖÎöͼ1£º×Ó¶þ´úµÄÐÔ×´·ÖÀë±ÈΪ12£º3£º1£¬ÊÇ¡°9£º3£º3£º1¡±µÄ±äʽ£¬ËµÃ÷¿ØÖƹ·Æ¤Ã«µÄÁ½¶Ô»ùÒòλÓÚÁ½¶Ô³£È¾É«ÌåÉÏ£¬ËüÃǵÄÒÅ´«×ñÑ»ùÒòµÄ×ÔÓÉ×éºÏ¶¨ÂÉ£®
·ÖÎöͼ2£º¢Ù±íʾ¼õÊýµÚÒ»´Î·ÖÁÑÖÐÆÚ£¬¢Ú±íʾ¼õÊýµÚ¶þ´Î·ÖÁѺóÆÚ£¬¢Û±íʾ¼õÊýµÚ¶þ´Î·ÖÁÑǰÆÚ£®
½â´ð ½â£º£¨1£©PÖкÖë¹·µÄ»ùÒòÐÍΪbbii£¬°×ë¹·»ùÒòÐÍΪBBII£¬F1Öа×ë¹·µÄ»ùÒòÐÍΪBbIi£¬ÔòF2Öа×ë¹·»ùÒòÐÍΪ$\frac{9}{16}$B_I_ºÍ$\frac{3}{16}$bbI_£¬ºÚë¹·µÄ»ùÒòÐÍΪ$\frac{3}{16}$B_ii£¬ºÖë¹·µÄ»ùÒòÐÍΪ$\frac{1}{16}$bbii£¬Òò´ËF2ÖУ¬ºÚë¹·µÄ»ùÒòÐͼ°¸ÅÂÊÊÇ$\frac{1}{3}$BBiiºÍ$\frac{2}{3}$Bbii£¬ÆäÖÐBµÄ»ùÒòƵÂÊΪ$\frac{1}{3}+\frac{2}{3}¡Á\frac{1}{2}$=$\frac{2}{3}$£¬bµÄ»ùÒòƵÂÊΪ$\frac{1}{3}$£¬ÈúÚë¹·×ÔÓɽ»Å䣬¸ù¾ÝÒÅ´«Æ½ºâ¶¨ÂÉ£¬ºó´úºÖë¹·£¨bbii£©±ÈÀýΪ$\frac{1}{3}¡Á\frac{1}{3}$=$\frac{1}{9}$£®Èç¹ûÈà F2ÖкÖë¹·£¨bbii£©Óë F1½»Å䣨BbIi£©£¬µÃµ½°×ë¹·£¨$\frac{1}{4}$BbIi¡¢$\frac{1}{4}$bbIi£©£ººÚë¹·£¨$\frac{1}{4}$Bbii£©£ººÖë¹·£¨$\frac{1}{4}$bbii£©=2£º1£º1£®
£¨2£©µÈλ»ùÒòBÓëbµÄ±¾ÖÊÇø±ðÆäÍÑÑõºËÜÕËᣨ¼î»ù£©ÅÅÁÐ˳Ðò²»Í¬£®
£¨3£©ÔÚ¼õÊýµÚ¶þ´Î·ÖÁѹý³ÌÖУ¬´Î¼¶ÂÑĸϸ°û·ÖÁÑʱϸ°ûÖʽøÐв»¾ùµÈµÄ·ÖÁÑ£¬²úÉúÒ»¸ö´óµÄÂÑϸ°ûºÍÒ»¸öСµÄ¼«Ì壬Òò´ËÖ»ÄܲúÉú1ÖÖ1¸öÂÑϸ°û£®
£¨4£©Ï¸°û¢Ù´¦ÓÚ¼õÊýµÚÒ»´Î·ÖÁÑÖÐÆÚ£¬Óëϸ°û¢Ú¡¢¢Û´æÔڵIJî±ðÊÇϸ°û¢Ùº¬ÓÐͬԴȾɫÌ壬ÇÒȾɫÌåÊýĿδ·¢Éú¼õ°ë£®
¹Ê´ð°¸Îª£º
£¨1£©$\frac{1}{9}$ °×ë¹·£ººÚë¹·£ººÖë¹·=2£º1£º1
£¨2£©¼î»ù¶ÔµÄÅÅÁÐ˳Ðò²»Í¬
£¨3£©Í¼ÖбêºÅ¢ÚµÄϸ°ûµÄ²»¾ùµÈ·ÖÁÑ
£¨4£©Ï¸°û¢Û²»º¬ÓÐͬԴȾɫÌ壬ÇÒȾɫÌåÊýÄ¿¼õ°ë
µãÆÀ ±¾Ìâ½áºÏͼ½â£¬¿¼²éϸ°ûµÄ¼õÊý·ÖÁÑ¡¢»ùÒò×ÔÓÉ×éºÏ¶¨ÂɵÄʵÖʼ°Ó¦Óã¬ÒªÇó¿¼Éúʶ¼Çϸ°û¼õÊý·ÖÁѲ»Í¬Ê±ÆÚµÄÌØµã£¬ÄÜ׼ȷÅжÏͼÖи÷ϸ°ûµÄ·ÖÁÑ·½Ê½¼°Ëù´¦µÄʱÆÚ£»ÕÆÎÕ»ùÒò×ÔÓÉ×éºÏ¶¨ÂɵÄʵÖʼ°Ó¦Óã¬ÄÜ·ÖÎöÒÅ´«Í¼½â£¬ÔÙ½áºÏËùѧµÄ֪ʶ׼ȷ´ðÌ⣮
| | ÓðÉ« | ·ôÉ« | à¹É« |
| Á¬³Ç°×Ѽ | °×É« | °×É« | ºÚÉ« |
| °×¸ÄѼ | °×É« | °×É« | ³È»ÆÉ« |
£¨2£©Ñо¿ÈËÔ±¼ÙÉèÒ»¶ÔµÈλ»ùÒò¿ØÖƺÚÉ«ËØºÏ³É£¨Ó÷ûºÅB£®b±íʾ£¬B±íʾÄܺϳɺÚÉ«ËØ£©£¬ÁíÒ»¶ÔµÈλ»ùÒòÓëºÚÉ«ËØÔÚÓðëÖеıí´ïÓйأ¨ÓÃR£¬r±íʾ£¬r±íʾÒÖÖÆºÚÉ«ËØÔÚÓðëÖеıí´ï£©£®Á½¶ÔµÈλ»ùÒò¶¼Î»ÓÚ³£È¾É«ÌåÉÏ£®¸ù¾ÝÁ¬³Ç°×Ѽà¹É«ÎªºÚÉ«£¬¶ø°×¸ÄѼà¹É«²»ÏÔÏÖºÚÉ«ÍÆ²â£¬ÉÏÊöÔÓ½»ÊµÑéÖÐÁ¬³Ç°×ѼµÄ»ùÒòÐÍΪBBrr£¬°×¸ÄѼµÄ»ùÒòÐÍΪbbRR£¬F2´úÖа×ÓðѼµÄ»ùÒòÐÍÓÐ5 ÖÖ£¬·Ç°×ÓðѼÖÐÔÓºÏ×ӵıÈÀýΪ$\frac{8}{9}$£®
£¨3£©Ñо¿ÈËÔ±·¢ÏÖF2ºÚÓ𣺻ÒÓð=1£º2£¬ËûÃǼÙÉèR»ùÒò´æÔÚ¼ÁÁ¿Ð§Ó¦£¬º¬Ò»¸öR»ùÒò±íÏÖΪ»ÒÉ«£¬Á½¸öR»ùÒò±íÏÖΪºÚÉ«£¬ÎªÁËÑéÖ¤¸Ã¼ÙÉ裬ËûÃǽ«Fl»ÒÓðѼÓëÇ×±¾Öеİ׸ÄѼ½øÐÐÔÓ½»£¬¹Û²ìͳ¼ÆÔÓ½»½á¹û£¬²¢¼ÆËã±ÈÀý£®
¢ÙÈôÔÓ½»½á¹ûΪºÚÓ𣺻ÒÓ𣺰×Óð=1£º1£º2£¬Ôò¼ÙÉè³ÉÁ¢£®
¢ÚÈôÔÓ½»½á¹ûΪ»ÒÓ𣺰×Óð=1£º1£¬Ôò¼ÙÉè²»³ÉÁ¢£®
| ×é±ð | Ç×±¾×é | F1µÄ±íÏÖÐͼ°±ÈÀý | |||||
| ×Ï»¨¿íÒ¶ | ·Û»¨¿íÒ¶ | °×»¨¿íÒ¶ | ×Ï»¨ÕÒ¶ | ·Û»¨ÕÒ¶ | °×»¨ÕÒ¶ | ||
| ¼× | ×Ï»¨¿íÒ¶¡Á×Ï»¨ÕÒ¶ | $\frac{9}{32}$ | $\frac{3}{32}$ | $\frac{4}{32}$ | $\frac{9}{32}$ | $\frac{3}{32}$ | $\frac{4}{32}$ |
| ÒÒ | ×Ï»¨¿íÒ¶¡Á°×»¨¿íÒ¶ | $\frac{9}{16}$ | $\frac{3}{16}$ | 0 | $\frac{3}{16}$ | $\frac{1}{16}$ | 0 |
| ±û | ·Û»¨¿íÒ¶¡Á·Û»¨ÕÒ¶ | 0 | $\frac{3}{8}$ | $\frac{1}{8}$ | 0 | $\frac{3}{8}$ | $\frac{1}{8}$ |
£¨2£©¸ù¾Ý±íÖÐÒÒÔÓ½»×éºÏ£¬¿ÉÅжÏҶƬ¿í¶ÈÕâÒ»ÐÔ×´ÖеÄÕÒ¶ÊÇÒþÐÔÐÔ×´£®
£¨3£©Èô¼××éÖеÄ×Ï»¨¿íÒ¶Ç×±¾×Ô½»£¬Ôò²úÉúµÄ×Ó´úÖ²ÖêÀíÂÛÉÏÓ¦ÓÐ6ÖÖ±íÏÖÐÍ£¬ÆäÖзۻ¨¿íÒ¶Ö²ÖêÕ¼µÄ±ÈÀýΪ$\frac{3}{32}$£®
£¨4£©ÈôÖ»¿¼ÂÇ»¨É«µÄÒÅ´«£®¼××éµÄF1ÖÐ×Ô½»²»»á·¢ÉúÐÔ×´·ÖÀëµÄ¸öÌåÕ¼$\frac{1}{4}$£®ÈÃÒÒ×é²úÉúµÄF1ÖÐÈ«²¿×Ï»¨Ö²Öê×Ô»¨´«·Û£¬ÔÚÿÖê×Ï»¨Ö²Öê²úÉúµÄ×Ó´úÊýÁ¿ÏàµÈÇÒ×ã¹»¶àµÄÇé¿öÏ£¬Æä×Ó´úÖ²ÖêµÄ»ùÒòÐ͹²ÓÐ9ÖÖ£¬ÆäÖзۻ¨Ö²ÖêÕ¼µÄ±ÈÀýΪ$\frac{1}{8}$£®
| A£® | ´ÆÐÛ¹ûÓ¬µÄ»ùÒòÐÍ·Ö±ðΪAaXRXrºÍAaXrY | |
| B£® | ¸Ã¶Ô¹ûÓ¬ÔÓ½»ºóµÃµ½µÄF1´úÖдƹûÓ¬ÖÐÔÓºÏ×ÓËùÕ¼µÄ±ÈÀýΪ$\frac{3}{4}$ | |
| C£® | »ùÒòAºÍaµÄ¸ù±¾Çø±ðÊǼî»ù¶ÔµÄÅÅÁÐ˳Ðò²»Í¬ | |
| D£® | ¢òºÅ¢óºÅȾɫÌåÔÚ¼õÊýµÚÒ»´Î·ÖÁѵÄËÄ·ÖÌåʱÆÚ·¢Éú½»²æ»¥»» |
| A£® | ºÚɫèÓëçéè£Ã¨ÔÓ½»µÄºó´úÖÐÓÐ$\frac{1}{4}$µÄ»ÆÃ¨ | |
| B£® | çéè£Ã¨Óë»ÆÃ¨ÔÓ½»ºó´úÖÐçéè£Ã¨Õ¼$\frac{1}{4}$ | |
| C£® | Ϊ³ÖÐø¸ßЧµØ·±Ö³çéè£Ã¨£¬Ó¦Öð´úÌÔÌÆäËûÌåÉ«µÄè | |
| D£® | Ö»ÓкÚèºÍ»ÆÃ¨ÔÓ½»£¬²ÅÄÜ»ñµÃ×î´ó±ÈÀýµÄçéè£Ã¨ |