Question

11£®ÒÑÖª´üÖÐ×°ÓдóСÏàͬµÄ2¸ö°×Çò£¬2¸öºìÇòºÍ1¸ö»ÆÇò£®Ò»ÏîÓÎÏ·¹æ¶¨£ºÃ¿¸ö°×Çò¡¢ºìÇòºÍ»ÆÇòµÄ·ÖÖµ·Ö±ðÊÇ0·Ö¡¢1·ÖºÍ2·Ö£¬Ã¿Ò»¾Ö´Ó´üÖÐÒ»´ÎÐÔÈ¡³öÈý¸öÇò£¬½«3¸öÇò¶ÔÓ¦µÄ·ÖÖµÏà¼Óºó³ÆΪ¸Ã¾ÖµÄµÃ·Ö£¬¼ÆËãÍêµÃ·Öºó½«Çò·Å»Ø´üÖУ®µ±³öÏÖµÚn¾ÖµÃn£¨n¡ÊN^*£©·ÖµÄÇé¿ö¾ÍËãÓÎÏ·¹ý¹Ø£¬Í¬Ê±ÓÎÏ·½áÊø£¬ÈôËľֹýºóÈÔδ¹ý¹Ø£¬ÓÎÏ·Ò²½áÊø£®
£¨1£©ÇóÔÚÒ»¾ÖÓÎÏ·ÖеÃ3·ÖµÄ¸ÅÂÊ£»
£¨2£©ÇóÓÎÏ·½áÊøʱ¾ÖÊýXµÄ·Ö²¼ÁкÍÊýѧÆÚÍûE£¨X£©£®

Answer 1

·ÖÎö £¨¢ñ£©¸ù¾ÝÏ໥¶ÀÁ¢Ê¼þµÄ¸ÅÂʹ«Ê½Çó³ö¶ÔÓ¦µÄ¸ÅÂÊÖµ£»
£¨¢ò£©ÓÉÌâÒâÖªËæ»ú±äÁ¿XµÄ¿ÉÄÜÈ¡Öµ£¬¼ÆËãÔÚÒ»¾ÖÓÎÏ·ÖеÃ2·ÖµÄ¸ÅÂÊÖµ£¬
Çó³ö¶ÔÓ¦µÄ¸ÅÂÊÖµ£¬Ð´³ö·Ö²¼ÁУ¬¼ÆËãÊýѧÆÚÍû£®

½â´ð ½â£º£¨¢ñ£©ÉèÔÚÒ»¾ÖÓÎÏ·ÖеÃ3·ÖΪʼþA£¬
ÔòP£¨A£©=$\frac{{C}_{2}^{1}{•C}_{2}^{1}{•C}_{1}^{1}}{{C}_{5}^{3}}$=$\frac{2}{5}$£»
£¨¢ò£©ÓÉÌâÒâËæ»ú±äÁ¿XµÄ¿ÉÄÜȡֵΪ1£¬2£¬3£¬4£»
ÇÒÔÚÒ»¾ÖÓÎÏ·ÖеÃ2·ÖµÄ¸ÅÂÊΪ$\frac{{C}_{2}^{1}{•C}_{2}^{2}{+C}_{2}^{2}{•C}_{1}^{1}}{{C}_{5}^{3}}$=$\frac{3}{10}$£»
ÔòP£¨X=1£©=$\frac{{C}_{2}^{2}{•C}_{2}^{1}}{{C}_{5}^{3}}$=$\frac{1}{5}$£¬
P£¨X=2£©=$\frac{4}{5}$¡Á$\frac{3}{10}$=$\frac{6}{25}$£¬
P£¨X=3£©=$\frac{4}{5}$¡Á£¨1-$\frac{3}{10}$£©¡Á$\frac{2}{5}$=$\frac{28}{125}$£¬
P£¨X=4£©=$\frac{4}{5}$¡Á£¨1-$\frac{3}{10}$£©¡Á$\frac{3}{5}$=$\frac{42}{125}$£¬
¡àXµÄ·Ö²¼ÁÐΪ£º

X	1	2	3	4
P	$\frac{1}{5}$	$\frac{6}{25}$	$\frac{28}{125}$	$\frac{42}{125}$

EX=1¡Á$\frac{1}{5}$+2¡Á$\frac{6}{25}$+3¡Á$\frac{28}{125}$+4¡Á$\frac{42}{125}$=$\frac{337}{125}$£®

µãÆÀ ±¾Ì⿼²éÁËÏ໥¶ÀÁ¢Ê¼þ¸ÅÂÊÒÔ¼°ÀëÉ¢ÐÍËæ»ú±äÁ¿µÄ·Ö²¼ÁкÍÊýѧÆÚÍûµÄ¼ÆËãÎÊÌ⣬ÊÇÖеµÌ⣮