向高手求助一道建模题目的思路.

bestsky

<p >问题描述如下:

有18支足球队要进行9场比赛.为此,彩票公司发行足球彩票,10元一张.每张彩票只能填写9个数字,猜9场比赛中主队的胜,平,负.数字3表示胜,1表示平,0表示负.公司决定,仅设特等奖和一等奖.并规定,全部猜中了9场比赛结果的彩票即得特等奖,奖金100000元.9场比赛中仅猜错一场比赛结果的彩票获得一等奖,奖金10000元.</p>


<p >根据查阅的有关资料,按照各场比赛对阵双方的历史比赛战绩统计结果,主队以往胜,平的比例如表1</p>


<p align="center" style="text-align: center; text-indent: 21pt;">表1  各场比赛对阵双方的历史成绩统计结果</p>


<div align="center">

<table border="1" cellspacing="0" cellpadding="0" style="border: medium none ; border-collapse: collapse;">
<tr >
  <td valign="top" style="border: 1pt solid windowtext; padding: 0cm 5.4pt;">
  <p>场次</p>
  </td>
  <td valign="top" style="border-style: solid solid solid none; border-width: 1pt 1pt 1pt medium; border-top: 1pt solid windowtext; border-right: 1pt solid windowtext; border-bottom: 1pt solid windowtext; padding: 0cm 5.4pt;">
  <p>1</p>
  </td>
  <td valign="top" style="border-style: solid solid solid none; border-width: 1pt 1pt 1pt medium; border-top: 1pt solid windowtext; border-right: 1pt solid windowtext; border-bottom: 1pt solid windowtext; padding: 0cm 5.4pt;">
  <p>2</p>
  </td>
  <td valign="top" style="border-style: solid solid solid none; border-width: 1pt 1pt 1pt medium; border-top: 1pt solid windowtext; border-right: 1pt solid windowtext; border-bottom: 1pt solid windowtext; padding: 0cm 5.4pt;">
  <p>3</p>
  </td>
  <td valign="top" style="border-style: solid solid solid none; border-width: 1pt 1pt 1pt medium; border-top: 1pt solid windowtext; border-right: 1pt solid windowtext; border-bottom: 1pt solid windowtext; padding: 0cm 5.4pt;">
  <p>4</p>
  </td>
  <td valign="top" style="border-style: solid solid solid none; border-width: 1pt 1pt 1pt medium; border-top: 1pt solid windowtext; border-right: 1pt solid windowtext; border-bottom: 1pt solid windowtext; padding: 0cm 5.4pt;">
  <p>5</p>
  </td>
  <td valign="top" style="border-style: solid solid solid none; border-width: 1pt 1pt 1pt medium; border-top: 1pt solid windowtext; border-right: 1pt solid windowtext; border-bottom: 1pt solid windowtext; padding: 0cm 5.4pt;">
  <p>6</p>
  </td>
  <td valign="top" style="border-style: solid solid solid none; border-width: 1pt 1pt 1pt medium; border-top: 1pt solid windowtext; border-right: 1pt solid windowtext; border-bottom: 1pt solid windowtext; padding: 0cm 5.4pt;">
  <p>7</p>
  </td>
  <td valign="top" style="border-style: solid solid solid none; border-width: 1pt 1pt 1pt medium; border-top: 1pt solid windowtext; border-right: 1pt solid windowtext; border-bottom: 1pt solid windowtext; padding: 0cm 5.4pt;">
  <p>8</p>
  </td>
  <td valign="top" style="border-style: solid solid solid none; border-width: 1pt 1pt 1pt medium; border-top: 1pt solid windowtext; border-right: 1pt solid windowtext; border-bottom: 1pt solid windowtext; padding: 0cm 5.4pt;">
  <p>9</p>
  </td>
</tr>
<tr >
  <td valign="top" style="border-style: none solid solid; border-width: medium 1pt 1pt; border-left: 1pt solid windowtext; border-right: 1pt solid windowtext; border-bottom: 1pt solid windowtext; padding: 0cm 5.4pt;">
  <p>主队胜</p>
  </td>
  <td valign="top" style="border-style: none solid solid none; border-width: medium 1pt 1pt medium; border-right: 1pt solid windowtext; border-bottom: 1pt solid windowtext; padding: 0cm 5.4pt;">
  <p>0.35</p>
  </td>
  <td valign="top" style="border-style: none solid solid none; border-width: medium 1pt 1pt medium; border-right: 1pt solid windowtext; border-bottom: 1pt solid windowtext; padding: 0cm 5.4pt;">
  <p>0.67</p>
  </td>
  <td valign="top" style="border-style: none solid solid none; border-width: medium 1pt 1pt medium; border-right: 1pt solid windowtext; border-bottom: 1pt solid windowtext; padding: 0cm 5.4pt;">
  <p>0.5</p>
  </td>
  <td valign="top" style="border-style: none solid solid none; border-width: medium 1pt 1pt medium; border-right: 1pt solid windowtext; border-bottom: 1pt solid windowtext; padding: 0cm 5.4pt;">
  <p>0.15</p>
  </td>
  <td valign="top" style="border-style: none solid solid none; border-width: medium 1pt 1pt medium; border-right: 1pt solid windowtext; border-bottom: 1pt solid windowtext; padding: 0cm 5.4pt;">
  <p>0.28</p>
  </td>
  <td valign="top" style="border-style: none solid solid none; border-width: medium 1pt 1pt medium; border-right: 1pt solid windowtext; border-bottom: 1pt solid windowtext; padding: 0cm 5.4pt;">
  <p>0.62</p>
  </td>
  <td valign="top" style="border-style: none solid solid none; border-width: medium 1pt 1pt medium; border-right: 1pt solid windowtext; border-bottom: 1pt solid windowtext; padding: 0cm 5.4pt;">
  <p>0.39</p>
  </td>
  <td valign="top" style="border-style: none solid solid none; border-width: medium 1pt 1pt medium; border-right: 1pt solid windowtext; border-bottom: 1pt solid windowtext; padding: 0cm 5.4pt;">
  <p>0.25</p>
  </td>
  <td valign="top" style="border-style: none solid solid none; border-width: medium 1pt 1pt medium; border-right: 1pt solid windowtext; border-bottom: 1pt solid windowtext; padding: 0cm 5.4pt;">
  <p>0.1</p>
  </td>
</tr>
<tr >
  <td valign="top" style="border-style: none solid solid; border-width: medium 1pt 1pt; border-left: 1pt solid windowtext; border-right: 1pt solid windowtext; border-bottom: 1pt solid windowtext; padding: 0cm 5.4pt;">
  <p>主队平</p>
  </td>
  <td valign="top" style="border-style: none solid solid none; border-width: medium 1pt 1pt medium; border-right: 1pt solid windowtext; border-bottom: 1pt solid windowtext; padding: 0cm 5.4pt;">
  <p>0.25</p>
  </td>
  <td valign="top" style="border-style: none solid solid none; border-width: medium 1pt 1pt medium; border-right: 1pt solid windowtext; border-bottom: 1pt solid windowtext; padding: 0cm 5.4pt;">
  <p>0.33</p>
  </td>
  <td valign="top" style="border-style: none solid solid none; border-width: medium 1pt 1pt medium; border-right: 1pt solid windowtext; border-bottom: 1pt solid windowtext; padding: 0cm 5.4pt;">
  <p>0.3</p>
  </td>
  <td valign="top" style="border-style: none solid solid none; border-width: medium 1pt 1pt medium; border-right: 1pt solid windowtext; border-bottom: 1pt solid windowtext; padding: 0cm 5.4pt;">
  <p>0.45</p>
  </td>
  <td valign="top" style="border-style: none solid solid none; border-width: medium 1pt 1pt medium; border-right: 1pt solid windowtext; border-bottom: 1pt solid windowtext; padding: 0cm 5.4pt;">
  <p>0.7</p>
  </td>
  <td valign="top" style="border-style: none solid solid none; border-width: medium 1pt 1pt medium; border-right: 1pt solid windowtext; border-bottom: 1pt solid windowtext; padding: 0cm 5.4pt;">
  <p>0.25</p>
  </td>
  <td valign="top" style="border-style: none solid solid none; border-width: medium 1pt 1pt medium; border-right: 1pt solid windowtext; border-bottom: 1pt solid windowtext; padding: 0cm 5.4pt;">
  <p>0.5</p>
  </td>
  <td valign="top" style="border-style: none solid solid none; border-width: medium 1pt 1pt medium; border-right: 1pt solid windowtext; border-bottom: 1pt solid windowtext; padding: 0cm 5.4pt;">
  <p>0.6</p>
  </td>
  <td valign="top" style="border-style: none solid solid none; border-width: medium 1pt 1pt medium; border-right: 1pt solid windowtext; border-bottom: 1pt solid windowtext; padding: 0cm 5.4pt;">
  <p>0.7</p>
  </td>
</tr>
</table>

</div>


<p ><p> </p></p>


<p ><!--[if !supportLists]-->(1)                 
<!--[endif]-->一个人至少要买几张彩票,每张彩票应如何填写(至少列出500张彩票应填写的数字),才能使他获得特等奖的可能性不低于90%?这是,如果他获得特等奖,他是赚还是赔?<p></p></p>


<p ><!--[if !supportLists]-->(2)                  
<!--[endif]-->如果一个人买了1000张彩票,他获得特等奖的最大可能性是多少&gt;并列出这些彩票应填写的数字.<p></p></p>


<p ><!--[if !supportLists]-->(3)                  
<!--[endif]-->一个人至少要买几张彩票,每张彩票应如何填写,才能保证他100%获奖?这是如果他获得一等奖,他是赔钱还是赚钱?<p></p></p>


<p ><!--[if !supportLists]-->(4)                  
<!--[endif]-->一个人买了一张彩票应如何填写才能使获奖的可能性最大?这个最大可能性是多大?这时,他可能获得的平均奖金是多少?<p></p></p>


<p ><!--[if !supportLists]-->(5)                  
<!--[endif]-->对一般情况进行讨论.

只求高手给出思路,谢谢!

</p>
<p ><p></p></p>