Question

19£®¼×¡¢ÒÒÁ½Ö§ÅÅÇò¶Ó½øÐбÈÈü£¬Ô¼¶¨ÏÈʤ3¾ÖÕß»ñµÃ±ÈÈüµÄʤÀû£¬±ÈÈüËæ¼´½áÊø£®³ýµÚÎå¾Ö¼×¶Ó»ñʤµÄ¸ÅÂÊÊÇ$\frac{1}{2}$Í⣬ÆäÓàÿ¾Ö±ÈÈü¼×¶Ó»ñʤµÄ¸ÅÂʶ¼ÊÇ$\frac{2}{3}$£®¼ÙÉè¸÷¾Ö±ÈÈü½á¹ûÏ໥¶ÀÁ¢£®
£¨1£©·Ö±ðÇó¼×¶ÓÒÔ3£º0£¬3£º1£¬3£º2»ñʤµÄ¸ÅÂÊ£»
£¨2£©Èô±ÈÈü½á¹ûΪ3£º0»ò3£º1£¬ÔòʤÀû·½µÃ3·Ö¡¢¶Ô·½µÃ0·Ö£»Èô±ÈÈü½á¹ûΪ3£º2£¬ÔòʤÀû·½µÃ2·Ö¡¢¶Ô·½µÃ1·Ö£®Çó¼×¶ÓµÃ·ÖXµÄ¸ÅÂÊ·Ö²¼¼°ÊýѧÆÚÍû£®

Answer 1

·ÖÎö £¨1£©¼×¶Ó»ñʤÓÐÈýÖÖÇéÐΣ¬¢Ù3£º0£¬¢Ú3£º1£¬¢Û3£º2£¬ÆäÿÖÖÇéÐεÄ×îºóÒ»¾Ö¿Ï¶¨ÊǼ׶Óʤ£¬·Ö±ðÇó³öÏàÓ¦µÄ¸ÅÂÊ£¬×îºó¸ù¾Ý»¥³âʼþµÄ¸ÅÂʹ«Ê½Çó³ö¼×¶Ó»ñµÃÕâ´Î±ÈÈüʤÀûµÄ¸ÅÂÊ£»
£¨2£©XµÄÈ¡Öµ¿ÉÄÜΪ0£¬1£¬2£¬3£¬È»ºóÀûÓÃÏ໥¶ÀÁ¢Ê¼þµÄ¸ÅÂʳ˷¨¹«Ê½Çó³öÏàÓ¦µÄ¸ÅÂÊ£¬Áгö·Ö²¼ÁУ¬×îºó¸ù¾ÝÊýѧÆÚÍû¹«Ê½½âÖ®¼´¿É£®

½â´ð ½â£º£¨1£©¼Ç¼×¶ÓÒÔ3£º0£¬3£º1£¬3£º2»ñʤ·Ö±ðΪʼþA£¬B£¬C£®
ÓÉÌâÒâµÃP£¨A£©=$£¨\frac{2}{3}£©^{3}=\frac{8}{27}$£¬
P£¨B£©=${C}_{3}^{2}£¨\frac{2}{3}£©^{2}•£¨\frac{1}{3}£©•£¨\frac{2}{3}£©=\frac{8}{27}$£¬
P£¨C£©=${C}_{4}^{2}£¨\frac{2}{3}£©^{2}•£¨\frac{1}{3}£©^{2}•\frac{1}{2}=\frac{4}{27}$
£¨2£©XµÄ¿ÉÄÜȡֵΪ0£¬1£¬2£¬3£®
P£¨X=3£©=P£¨A£©+P£¨B£©=$\frac{16}{27}$£»  P£¨X=2£©=P£¨C£©=$\frac{4}{27}$£¬
P£¨X=1£©=C${\;}_{4}^{2}$•£¨$\frac{2}{3}$£©²£¨$\frac{1}{3}$£©²•$\frac{1}{2}$=$\frac{4}{27}$£¬P£¨X=0£©=1-P£¨1¡ÜX¡Ü3£©=$\frac{1}{9}$£®
ËùÒÔXµÄ·Ö²¼ÁÐΪ£º

X	0	1	2	3
P	$\frac{1}{9}$	$\frac{4}{27}$	$\frac{4}{27}$	$\frac{16}{27}$

´Ó¶øE£¨X£©=0¡Á$\frac{1}{9}$+1¡Á$\frac{4}{27}$+2¡Á$\frac{4}{27}$+3¡Á$\frac{16}{27}$=$\frac{20}{9}$£®
´ð£º¼×¶ÓÒÔ3£º0£¬3£º1£¬3£º2»ñʤµÄ¸ÅÂÊ·Ö±ðΪ$\frac{8}{27}$£¬$\frac{8}{27}$£¬$\frac{4}{27}$£®¼×¶ÓµÃ·ÖXµÄÊýѧÆÚÍûΪ$\frac{20}{9}$£®  ¡­£¨10·Ö£©

µãÆÀ ±¾ÌâÖ÷Òª¿¼²éÁËÏ໥¶ÀÁ¢Ê¼þµÄ¸ÅÂʳ˷¨¹«Ê½£¬ÒÔ¼°ÀëÉ¢ÐÍËæ»ú±äÁ¿µÄÆÚÍûÓë·Ö²¼ÁУ¬Í¬Ê±¿¼²éÁË·ÖÀàÌÖÂÛµÄÊýѧ˼Ï룬ÊôÓÚÖеµÌ⣮