Question

3£®Ä³Ð¡Ñ§¶ÔÎåÄ꼶µÄѧÉú½øÐÐÌåÖʲâÊÔ£¬ÒÑÖªÎåÄêÒ»°à¹²ÓÐѧÉú30ÈË£¬²âÊÔÁ¢¶¨ÌøÔ¶µÄ³É¼¨Óþ¥Ò¶Í¼±íʾÈçͼ£¨µ¥Î»£ºcm£©£º
ÄÐÉú³É¼¨ÔÚ175cmÒÔÉÏ£¨°üÀ¨175cm£©¶¨ÒåΪ¡°ºÏ¸ñ¡±£¬³É¼¨ÔÚ175cmÒÔÏ£¨²»°üÀ¨175cm£©¶¨ÒåΪ¡°²»ºÏ¸ñ¡±£®
Å®Éú³É¼¨ÔÚ165cmÒÔÉÏ£¨°üÀ¨165cm£©¶¨ÒåΪ¡°ºÏ¸ñ¡±£¬³É¼¨ÔÚ165cmÒÔÏ£¨²»°üÀ¨165cm£©¶¨ÒåΪ¡°²»ºÏ¸ñ¡±£®
£¨¢ñ£©ÇóÎåÄêÒ»°àµÄÅ®ÉúÁ¢¶¨ÌøÔ¶³É¼¨µÄÖÐλÊý£»
£¨¢ò£©ÔÚÎåÄêÒ»°àµÄÄÐÉúÖÐÈÎÒâÑ¡È¡3ÈË£¬ÇóÖÁÉÙÓÐ2È˵ijɼ¨ÊǺϸñµÄ¸ÅÂÊ£»
£¨¢ó£©Èô´ÓÎåÄêÒ»°à³É¼¨¡°ºÏ¸ñ¡±µÄѧÉúÖÐÑ¡È¡2È˲μӸ´ÊÔ£¬ÓÃX±íʾÆäÖÐÄÐÉúµÄÈËÊý£¬Ð´³öXµÄ·Ö²¼ÁУ¬²¢ÇóXµÄÊýѧÆÚÍû£®

Answer 1

·ÖÎö £¨I£©Óɾ¥Ò¶Í¼ÄÜÇó³öÎåÄêÒ»°àµÄÅ®ÉúÁ¢¶¨ÌøÔ¶³É¼¨µÄÖÐλÊý£®
£¨II£©Éè¡°½öÓÐÁ½È˵ijɼ¨ºÏ¸ñ¡±ÎªÊ¼þA£¬¡°ÓÐÈýÈ˵ijɼ¨ºÏ¸ñ¡±ÎªÊ¼þB£¬ÖÁÉÙÓÐÁ½È˵ijɼ¨ÊǺϸñµÄ¸ÅÂÊ£ºP=P£¨A£©+P£¨B£©£¬ÓÉ´ËÄÜÇó³öÖÁÉÙÓÐ2È˵ijɼ¨ÊǺϸñµÄ¸ÅÂÊ£®
£¨III£©ÒòΪŮÉú¹²ÓÐ18ÈË£¬ÆäÖÐÓÐ10È˺ϸñ£¬ÒÀÌâÒ⣬XµÄȡֵΪ0£¬1£¬2£¬·Ö±ðÇó³öÏàÓ¦µÄ¸ÅÂÊ£¬ÓÉ´ËÄÜÇó³öXµÄ·Ö²¼ÁкÍXµÄÊýѧÆÚÍû£®

½â´ð ½â£º£¨I£©Óɾ¥Ò¶Í¼µÃÎåÄêÒ»°àµÄÅ®ÉúÁ¢¶¨ÌøÔ¶³É¼¨µÄÖÐλÊýΪ$\frac{165+168}{2}=166.5$cm£®¡­£¨2·Ö£©
£¨II£©Éè¡°½öÓÐÁ½È˵ijɼ¨ºÏ¸ñ¡±ÎªÊ¼þA£¬¡°ÓÐÈýÈ˵ijɼ¨ºÏ¸ñ¡±ÎªÊ¼þB£¬
ÖÁÉÙÓÐÁ½È˵ijɼ¨ÊǺϸñµÄ¸ÅÂÊ£ºP=P£¨A£©+P£¨B£©£¬
ÓÖÄÐÉú¹²12ÈË£¬ÆäÖÐÓÐ8È˺ϸñ£¬´Ó¶ø$P£¨A£©=\frac{C_4^1•C_8^2}{{C{\;}_{12}^3}}$£¬£¨4·Ö£©
$P£¨B£©=\frac{C_8^3}{{C{\;}_{12}^3}}$£¬ËùÒÔ$p=\frac{42}{55}$£®£¨6·Ö£©
£¨III£©ÒòΪŮÉú¹²ÓÐ18ÈË£¬ÆäÖÐÓÐ10È˺ϸñ£¬
ÒÀÌâÒ⣬XµÄȡֵΪ0£¬1£¬2£®
Ôò$P£¨X=0£©=\frac{{C_8^0C_{10}^2}}{{C_{18}^2}}=\frac{5}{17}$£¬
$P£¨X=1£©=\frac{{C_8^1C_{10}^1}}{{C_{18}^2}}=\frac{80}{153}$£¬
$P£¨X=2£©=\frac{{C_8^2C_{10}^0}}{{C_{18}^2}}=\frac{28}{153}$£¬
£¨Ã¿Ïî1·Ö£©£¨10·Ö£©
Òò´Ë£¬XµÄ·Ö²¼ÁÐÈçÏ£º

X	0	1	2
P	$\frac{5}{17}$	$\frac{80}{153}$	$\frac{28}{153}$

¡à$E£¨X£©=0¡Á\frac{5}{17}+1¡Á\frac{80}{153}+2¡Á\frac{28}{153}=\frac{136}{153}=\frac{8}{9}$£¨ÈË£©£®£¨Î´»¯¼ò²»¿Û·Ö£©£¨12·Ö£©
£¨»òÊÇ£¬ÒòΪX·þ´Ó³¬¼¸ºÎ·Ö²¼£¬ËùÒÔ$E£¨X£©=2¡Á\frac{8}{18}=\frac{8}{9}$£¨ÈË£©£®

µãÆÀ ±¾Ì⿼²éÖÐλÊý¡¢¸ÅÂÊ¡¢·Ö²¼ÁеÄÇ󷨣¬ÊÇÖеµÌ⣬½âÌâʱҪÈÏÕæÉóÌ⣬עÒâÅÅÁÐ×éºÏ֪ʶµÄºÏÀíÔËÓã®