Question

13£®ÂíÀ´Î÷ÑǺ½¿Õ¹«Ë¾3ÔÂ8ÈÕº½°àºÅΪMH370Ô­¶¨ÓɼªÂ¡Æ·ÉÍù±±¾©µÄ·É»úʧȥÁªÏµºóÇ£¶¯×ÅËùÓÐÈ˵ÄÐÄ£¬½ñÓÐÖйú¡¢ÃÀ¹ú¡¢Ô½ÄÏ¡¢ÂíÀ´Î÷ÑÇËĹú¶¼ÅɳöËÑÑ°²¿¶Ó£¬¼ÙÉèÖйúºÍÃÀ¹úÄܹ»µ¥¶ÀËÑÑ°µ½Ä¿±êµÄ¸ÅÂÊΪ$\frac{2}{3}$£¬Ô½ÄϺÍÂíÀ´Î÷ÑÇÄܹ»µ¥¶ÀËÑÑ°µ½Ä¿±êµÄ¸ÅÂÊ·Ö±ðΪ$\frac{1}{3}$ºÍ$\frac{1}{4}$£®
£¨1£©ÈôÖÁÉÙÓÐÈý¸ö¹ú¼ÒËø¶¨Í¬Ò»Ä¿±ê²ÅÄܶ϶¨¸ÃÄ¿±êΪ·É»ú³öʵص㣬ÇóËÑÑ°µ½Ä¿±êµÄ¸ÅÂÊ£®
£¨2£©¼ÇËÑÑ°µ½Ä¿±êµÄ¹ú¼ÒÊýΪËæ»ú±äÁ¿X£¬ÇóXµÄ·Ö²¼ÁÐÓëÊýѧÆÚÍû£®

Answer 1

·ÖÎö £¨1£©ÉèA±íʾ¡°Öйúµ¥¶ÀËÑÑ°µ½Ä¿±ê¡±£¬B±íʾ¡°ÃÀ¹úµ¥¶ÀËÑÑ°µ½Ä¿±ê¡±£¬C±íʾ¡°Ô½Äϵ¥¶ÀËÑÑ°µ½Ä¿±ê¡±£¬D±íʾ¡°ÂíÀ´Î÷Ñǵ¥¶ÀËÑÑ°µ½Ä¿±ê¡±£¬A¡¢B¡¢C¡¢DÏ໥¶ÀÁ¢£¬ÓÉÒÑÖªµÃP£¨A£©=P£¨B£©=$\frac{2}{3}$£¬P£¨C£©=$\frac{1}{3}$£¬P£¨D£©=$\frac{1}{4}$£¬ËÑÑ°µ½Ä¿±êµÄ¸ÅÂÊ£ºP=P£¨ABCD£©+P£¨$\overline{A}BCD$£©+P£¨A$\overline{B}$CD£©+P£¨AB$\overline{C}$D£©+P£¨ABC$\overline{D}$£©£¬ÓÉ´ËÄÜÇó³ö½á¹û£®
£¨2£©ÓÉÒÑÖªµÃXµÄ¿ÉÄÜȡֵΪ0£¬1£¬2£¬3£¬4£¬·Ö±ðÇó³öÏàÓ¦µÄ¸ÅÂÊ£¬ÓÉ´ËÄÜÇó³öXµÄ·Ö²¼ÁкÍÊýѧÆÚÍû£®

½â´ð ½â£º£¨1£©ÉèA±íʾ¡°Öйúµ¥¶ÀËÑÑ°µ½Ä¿±ê¡±£¬B±íʾ¡°ÃÀ¹úµ¥¶ÀËÑÑ°µ½Ä¿±ê¡±£¬
C±íʾ¡°Ô½Äϵ¥¶ÀËÑÑ°µ½Ä¿±ê¡±£¬D±íʾ¡°ÂíÀ´Î÷Ñǵ¥¶ÀËÑÑ°µ½Ä¿±ê¡±£¬
A¡¢B¡¢C¡¢DÏ໥¶ÀÁ¢£¬
ÓÉÒÑÖªµÃP£¨A£©=P£¨B£©=$\frac{2}{3}$£¬P£¨C£©=$\frac{1}{3}$£¬P£¨D£©=$\frac{1}{4}$£¬
¡ßÖÁÉÙÓÐÈý¸ö¹ú¼ÒËø¶¨Í¬Ò»Ä¿±ê²ÅÄܶ϶¨¸ÃÄ¿±êΪ·É»ú³öʵص㣬
¡àËÑÑ°µ½Ä¿±êµÄ¸ÅÂÊ£º
P=P£¨ABCD£©+P£¨$\overline{A}BCD$£©+P£¨A$\overline{B}$CD£©+P£¨AB$\overline{C}$D£©+P£¨ABC$\overline{D}$£©
=$\frac{2}{3}¡Á\frac{2}{3}¡Á\frac{1}{3}¡Á\frac{1}{4}$+$\frac{1}{3}¡Á\frac{2}{3}¡Á\frac{1}{3}¡Á\frac{1}{4}$+$\frac{2}{3}¡Á\frac{1}{3}¡Á\frac{1}{3}¡Á\frac{1}{4}$+$\frac{2}{3}¡Á\frac{2}{3}¡Á\frac{2}{3}¡Á\frac{1}{4}$+$\frac{2}{3}¡Á\frac{2}{3}¡Á\frac{1}{3}¡Á\frac{3}{4}$
=$\frac{7}{27}$£®
£¨2£©ÓÉÒÑÖªµÃXµÄ¿ÉÄÜȡֵΪ0£¬1£¬2£¬3£¬4£¬
P£¨X=0£©=$\frac{1}{3}¡Á\frac{1}{3}¡Á\frac{2}{3}¡Á\frac{3}{4}$=$\frac{6}{108}$£¬
P£¨X=1£©=$\frac{2}{3}¡Á\frac{1}{3}¡Á\frac{2}{3}¡Á\frac{3}{4}$+$\frac{1}{3}¡Á\frac{2}{3}¡Á\frac{2}{3}¡Á\frac{3}{4}$+$\frac{1}{3}¡Á\frac{1}{3}¡Á\frac{1}{3}¡Á\frac{3}{4}$+$\frac{1}{3}¡Á\frac{1}{3}¡Á\frac{2}{3}¡Á\frac{1}{4}$=$\frac{29}{108}$£¬
P£¨X=2£©=$\frac{2}{3}¡Á\frac{2}{3}¡Á\frac{2}{3}¡Á\frac{3}{4}$+$\frac{2}{3}¡Á\frac{1}{3}¡Á\frac{1}{3}¡Á\frac{3}{4}$+$\frac{2}{3}¡Á\frac{1}{3}¡Á\frac{2}{3}¡Á\frac{1}{4}$+$\frac{1}{3}¡Á\frac{2}{3}¡Á\frac{1}{3}¡Á\frac{3}{4}$+$\frac{1}{3}¡Á\frac{2}{3}¡Á\frac{2}{3}¡Á\frac{1}{4}$+$\frac{1}{3}¡Á\frac{1}{3}¡Á\frac{1}{3}¡Á\frac{1}{4}$=$\frac{45}{108}$£¬
P£¨X=3£©=$\frac{1}{3}¡Á\frac{2}{3}¡Á\frac{1}{3}¡Á\frac{1}{4}$+$\frac{2}{3}¡Á\frac{1}{3}¡Á\frac{1}{3}¡Á\frac{1}{4}$+$\frac{2}{3}¡Á\frac{2}{3}¡Á\frac{2}{3}¡Á\frac{1}{4}$+$\frac{2}{3}¡Á\frac{2}{3}¡Á\frac{1}{3}¡Á\frac{3}{4}$=$\frac{24}{108}$£¬
P£¨X=4£©=$\frac{2}{3}¡Á\frac{2}{3}¡Á\frac{1}{3}¡Á\frac{1}{4}$=$\frac{4}{108}$£¬
¡àXµÄ·Ö²¼ÁÐΪ£º

X	0	1	2	3	4
P	$\frac{6}{108}$	$\frac{29}{108}$	$\frac{45}{108}$	$\frac{24}{108}$	$\frac{4}{108}$

EX=$0¡Á\frac{6}{108}+1¡Á\frac{29}{108}$+$2¡Á\frac{45}{108}$+3¡Á$\frac{24}{108}+$$4¡Á\frac{4}{108}$=$\frac{23}{12}$£®

µãÆÀ ±¾Ì⿼²é¸ÅÂʵÄÇ󷨣¬¿¼²éÀëÉ¢ÐÍËæ»ú±äÁ¿µÄ·Ö²¼ÁкÍÊýѧÆÚÍûµÄÇ󷨣¬ÊÇÖеµÌ⣬½âÌâʱҪÈÏÕæÉóÌ⣬עÒâÏ໥¶ÀÁ¢Ê¼þ¸ÅÂʳ˷¨¹«Ê½ºÍ»¥³âʼþ¸ÅÂʼӷ¨¹«Ê½µÄºÏÀíÔËÓã®