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<span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:新宋体">现有</span></span><i><span style="line-height:150%"><span style="font-family:"Times New Roman"">A</span></span></i><span style="line-height:150%"><span style="font-family:新宋体">、</span></span><i><span style="line-height:150%"><span style="font-family:"Times New Roman"">B</span></span></i><span style="line-height:150%"><span style="font-family:新宋体">两个不透明袋子，分别装有</span></span><span style="line-height:150%"><span style="font-family:"Times New Roman"">3</span></span><span style="line-height:150%"><span style="font-family:新宋体">个除颜色外完全相同的小球．其中，</span></span><i><span style="line-height:150%"><span style="font-family:"Times New Roman"">A</span></span></i><span style="line-height:150%"><span style="font-family:新宋体">袋装有</span></span><span style="line-height:150%"><span style="font-family:"Times New Roman"">2</span></span><span style="line-height:150%"><span style="font-family:新宋体">个白球，</span></span><span style="line-height:150%"><span style="font-family:"Times New Roman"">1</span></span><span style="line-height:150%"><span style="font-family:新宋体">个红球；</span></span><i><span style="line-height:150%"><span style="font-family:"Times New Roman"">B</span></span></i><span style="line-height:150%"><span style="font-family:新宋体">袋装有</span></span><span style="line-height:150%"><span style="font-family:"Times New Roman"">2</span></span><span style="line-height:150%"><span style="font-family:新宋体">个红球，</span></span><span style="line-height:150%"><span style="font-family:"Times New Roman"">1</span></span><span style="line-height:150%"><span style="font-family:新宋体">个白球．</span></span></span></span></span><br /> <span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:新宋体">（</span></span><span style="line-height:150%"><span style="font-family:"Times New Roman"">1</span></span><span style="line-height:150%"><span style="font-family:新宋体">）将</span></span><i><span style="line-height:150%"><span style="font-family:"Times New Roman"">A</span></span></i><span style="line-height:150%"><span style="font-family:新宋体">袋摇匀，然后从</span></span><i><span style="line-height:150%"><span style="font-family:"Times New Roman"">A</span></span></i><span style="line-height:150%"><span style="font-family:新宋体">袋中随机取出一个小球，求摸出小球是白色的概率；</span></span></span></span></span><br /> <span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:新宋体">（</span></span><span style="line-height:150%"><span style="font-family:"Times New Roman"">2</span></span><span style="line-height:150%"><span style="font-family:新宋体">）小华和小林商定了一个游戏规则：从摇匀后的</span></span><i><span style="line-height:150%"><span style="font-family:"Times New Roman"">A</span></span></i><span style="line-height:150%"><span style="font-family:新宋体">，</span></span><i><span style="line-height:150%"><span style="font-family:"Times New Roman"">B</span></span></i><span style="line-height:150%"><span style="font-family:新宋体">两袋中随机摸出一个小球，摸出的这两个小球，若颜色相同，则小林获胜；若颜色不同，则小华获胜．请用列表法或画出树状图的方法说明这个游戏规则对双方是否公平．</span></span></span></span></span>
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<span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:新宋体">解：（</span></span><span style="line-height:150%"><span style="font-family:"Times New Roman"">1</span></span><span style="line-height:150%"><span style="font-family:新宋体">）共有</span></span><span style="line-height:150%"><span style="font-family:"Times New Roman"">3</span></span><span style="line-height:150%"><span style="font-family:新宋体">种等可能结果，而摸出白球的结果有</span></span><span style="line-height:150%"><span style="font-family:"Times New Roman"">2</span></span><span style="line-height:150%"><span style="font-family:新宋体">种</span></span></span></span></span><br /> <span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:新宋体">∴</span></span><i><span style="line-height:150%"><span style="font-family:"Times New Roman"">P</span></span></i><span style="line-height:150%"><span style="font-family:新宋体">（摸出白球）＝</span></span></span></span></span><img height="35" src="/uploads/meth/20210301/7d625eccd8072ab30c980f7a480cf09d.png" width="13" /><span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:新宋体">；</span></span></span></span></span><br /> <span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:新宋体">（</span></span><span style="line-height:150%"><span style="font-family:"Times New Roman"">2</span></span><span style="line-height:150%"><span style="font-family:新宋体">）根据题意，列表如下：</span></span></span></span></span> <table class="Table" style="margin-left:19px; border-collapse:collapse; border:none"> <tbody> <tr> <td style="border-bottom:1px solid black; width:138px; padding:2px 2px 2px 2px; border-top:1px solid black; border-right:1px solid black; border-left:1px solid black" valign="top"><span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><i><span lang="EN-US" style="line-height:150%"><span style="font-family:"Times New Roman"">A</span></span></i><span lang="EN-US" style="line-height:150%"><span style="font-family:"Times New Roman""> <i>B</i></span></span></span></span></span></td> <td style="border-bottom:1px solid black; width:138px; padding:2px 2px 2px 2px; border-top:1px solid black; border-right:1px solid black; border-left:none" valign="top"><span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"> <span style="line-height:150%"><span style="font-family:新宋体">红</span></span><span lang="EN-US" style="line-height:150%"><span style="font-family:"Times New Roman"">1</span></span></span></span></span></td> <td style="border-bottom:1px solid black; width:138px; padding:2px 2px 2px 2px; border-top:1px solid black; border-right:1px solid black; border-left:none" valign="top"><span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:新宋体">红</span></span><span lang="EN-US" style="line-height:150%"><span style="font-family:"Times New Roman"">2</span></span></span></span></span></td> <td style="border-bottom:1px solid black; width:138px; padding:2px 2px 2px 2px; border-top:1px solid black; border-right:1px solid black; border-left:none" valign="top"><span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:新宋体">白</span></span></span></span></span></td> </tr> <tr> <td style="border-bottom:1px solid black; width:138px; padding:2px 2px 2px 2px; border-top:none; border-right:1px solid black; border-left:1px solid black" valign="top"><span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:新宋体">白</span></span><span lang="EN-US" style="line-height:150%"><span style="font-family:"Times New Roman"">1</span></span></span></span></span></td> <td style="border-bottom:1px solid black; width:138px; padding:2px 2px 2px 2px; border-top:none; border-right:1px solid black; border-left:none" valign="top"><span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:新宋体">（白</span></span><span lang="EN-US" style="line-height:150%"><span style="font-family:"Times New Roman"">1</span></span><span style="line-height:150%"><span style="font-family:新宋体">，红</span></span><span lang="EN-US" style="line-height:150%"><span style="font-family:"Times New Roman"">1</span></span><span style="line-height:150%"><span style="font-family:新宋体">）</span></span></span></span></span></td> <td style="border-bottom:1px solid black; width:138px; padding:2px 2px 2px 2px; border-top:none; border-right:1px solid black; border-left:none" valign="top"><span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:新宋体">（白</span></span><span lang="EN-US" style="line-height:150%"><span style="font-family:"Times New Roman"">1</span></span><span style="line-height:150%"><span style="font-family:新宋体">，红</span></span><span lang="EN-US" style="line-height:150%"><span style="font-family:"Times New Roman"">2</span></span><span style="line-height:150%"><span style="font-family:新宋体">）</span></span></span></span></span></td> <td style="border-bottom:1px solid black; width:138px; padding:2px 2px 2px 2px; border-top:none; border-right:1px solid black; border-left:none" valign="top"><span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:新宋体">（白</span></span><span lang="EN-US" style="line-height:150%"><span style="font-family:"Times New Roman"">1</span></span><span style="line-height:150%"><span style="font-family:新宋体">，白）</span></span></span></span></span></td> </tr> <tr> <td style="border-bottom:1px solid black; width:138px; padding:2px 2px 2px 2px; border-top:none; border-right:1px solid black; border-left:1px solid black" valign="top"><span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:新宋体">白</span></span><span lang="EN-US" style="line-height:150%"><span style="font-family:"Times New Roman"">2</span></span></span></span></span></td> <td style="border-bottom:1px solid black; width:138px; padding:2px 2px 2px 2px; border-top:none; border-right:1px solid black; border-left:none" valign="top"><span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:新宋体">（白</span></span><span lang="EN-US" style="line-height:150%"><span style="font-family:"Times New Roman"">2</span></span><span style="line-height:150%"><span style="font-family:新宋体">，红</span></span><span lang="EN-US" style="line-height:150%"><span style="font-family:"Times New Roman"">1</span></span><span style="line-height:150%"><span style="font-family:新宋体">）</span></span></span></span></span></td> <td style="border-bottom:1px solid black; width:138px; padding:2px 2px 2px 2px; border-top:none; border-right:1px solid black; border-left:none" valign="top"><span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:新宋体">（白</span></span><span lang="EN-US" style="line-height:150%"><span style="font-family:"Times New Roman"">2</span></span><span style="line-height:150%"><span style="font-family:新宋体">，红</span></span><span lang="EN-US" style="line-height:150%"><span style="font-family:"Times New Roman"">2</span></span><span style="line-height:150%"><span style="font-family:新宋体">）</span></span></span></span></span></td> <td style="border-bottom:1px solid black; width:138px; padding:2px 2px 2px 2px; border-top:none; border-right:1px solid black; border-left:none" valign="top"><span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:新宋体">（白</span></span><span lang="EN-US" style="line-height:150%"><span style="font-family:"Times New Roman"">2</span></span><span style="line-height:150%"><span style="font-family:新宋体">，白）</span></span></span></span></span></td> </tr> <tr> <td style="border-bottom:1px solid black; width:138px; padding:2px 2px 2px 2px; border-top:none; border-right:1px solid black; border-left:1px solid black" valign="top"><span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:新宋体">红</span></span></span></span></span></td> <td style="border-bottom:1px solid black; width:138px; padding:2px 2px 2px 2px; border-top:none; border-right:1px solid black; border-left:none" valign="top"><span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:新宋体">（红，红</span></span><span lang="EN-US" style="line-height:150%"><span style="font-family:"Times New Roman"">1</span></span><span style="line-height:150%"><span style="font-family:新宋体">）</span></span></span></span></span></td> <td style="border-bottom:1px solid black; width:138px; padding:2px 2px 2px 2px; border-top:none; border-right:1px solid black; border-left:none" valign="top"><span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:新宋体">（红，红</span></span><span lang="EN-US" style="line-height:150%"><span style="font-family:"Times New Roman"">2</span></span><span style="line-height:150%"><span style="font-family:新宋体">）</span></span></span></span></span></td> <td style="border-bottom:1px solid black; width:138px; padding:2px 2px 2px 2px; border-top:none; border-right:1px solid black; border-left:none" valign="top"><span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:新宋体">（红，白）</span></span></span></span></span></td> </tr> </tbody> </table> <span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:新宋体">由上表可知，共有</span></span><span style="line-height:150%"><span style="font-family:"Times New Roman"">9</span></span><span style="line-height:150%"><span style="font-family:新宋体">种等可能结果，其中颜色不相同的结果有</span></span><span style="line-height:150%"><span style="font-family:"Times New Roman"">5</span></span><span style="line-height:150%"><span style="font-family:新宋体">种，颜色相同的结果有</span></span><span style="line-height:150%"><span style="font-family:"Times New Roman"">4</span></span><span style="line-height:150%"><span style="font-family:新宋体">种</span></span></span></span></span><br /> <span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:新宋体">∴</span></span><i><span style="line-height:150%"><span style="font-family:"Times New Roman"">P</span></span></i><span style="line-height:150%"><span style="font-family:新宋体">（颜色不相同）＝</span></span></span></span></span><img height="35" src="/uploads/meth/20210301/3cf8101814d2973560d8226ca206825c.png" width="13" /><span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:新宋体">，</span></span><i><span style="line-height:150%"><span style="font-family:"Times New Roman"">P</span></span></i><span style="line-height:150%"><span style="font-family:新宋体">（颜色相同）＝</span></span></span></span></span><img height="35" src="/uploads/meth/20210301/7fbfacd3e59df0156afac5d77786d9fa.png" width="13" /><br /> <span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:新宋体">∵</span></span></span></span></span><img height="35" src="/uploads/meth/20210301/7af272f9609a7d03e36be15960ce42ae.png" width="13" /><span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:新宋体">＜</span></span></span></span></span><img height="35" src="/uploads/meth/20210301/d6f46ded0ae3f64d289016b3874f6483.png" width="13" /><br /> <span style="font-size:10.5pt"><span style="line-height:150%"><span style="font-family:Calibri"><span style="line-height:150%"><span style="font-family:新宋体">∴这个游戏规则对双方不公平</span></span></span></span></span>
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