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  • 試卷總共有5道選擇題,其中只有一個(gè)答案是正確的.如果每題都是隨機(jī)選擇一個(gè)答案,求答對(duì)題數(shù)X的概率分布及至少答對(duì)兩題的概率

    試卷總共有5道選擇題,其中只有一個(gè)答案是正確的.如果每題都是隨機(jī)選擇一個(gè)答案,求答對(duì)題數(shù)X的概率分布及至少答對(duì)兩題的概率
    數(shù)學(xué)人氣:847 ℃時(shí)間:2020-02-05 11:10:12
    優(yōu)質(zhì)解答
    答對(duì)0個(gè)是:C50(其中5是下標(biāo),1是上標(biāo),下同)*(3/4)*(3/4)*(3/4)*(3/4)*(3/4)=243/1024
    答對(duì)1個(gè)是:C51*(1/4)*(3/4)*(3/4)*(3/4)*(3/4)=405/1024
    答對(duì)2個(gè)是:C52*(1/4)*(1/4)*(3/4)*(3/4)*(3/4)=270/1024
    答對(duì)3個(gè)是:C53*(1/4)*(1/4)*(1/4)*(3/4)*(3/4)=90/1024
    答對(duì)4個(gè)是:C54*(1/4)*(1/4)*(1/4)*(1/4)*(3/4)=15/1024
    答對(duì)5個(gè)是:C55*(1/4)*(1/4)*(1/4)*(1/4)*(1/4)=1/1024
    至少答對(duì)2個(gè)題:即為至多答對(duì)一個(gè)的反面,即1-答對(duì)1個(gè)的概率-答對(duì)0個(gè)的概率=1-243/1024-405/1024=376/1024=47/128
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