题干

某地最近出台一项机动车驾照考试规定:每位考试者一年之内最多有4次参加考试的机会,一量某次考试通过,便可领取驾照,不再参加以后的考试,否则就一直考到第4次为止如果李明决定参加驾照考试,设他每次参加考试通过的概率依次为0.6,0.7,0.8,0.9.求在一年内李明参加驾照考试次数ξ的分布列和ξ的期望,并求李明在一所内领到驾照的概率.
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答案(点此获取答案解析)

解:ξ的取值分别为1,2,3,4.

ξ=1,表明李明第一次参加驾照考试就通过了,

故P(ξ=1)=0.6

ξ=2,表明李明在第一次考试未通过,第二次通过了,

故P(ξ=2)=(1﹣0.6)×0.7=0.28

ξ=3,表明李明在第一、二次考试未通过,第三次通过了,故

P(ξ=3)=(1﹣0.6)×(1﹣0.7)×0.8=0.096.

ξ=4,表明李明在第一、二、三次考试都未通过,故

P(ξ=4)=(1﹣0.6)×(1

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