题干

购买某种保险,每个投保人每年度向保险公司交纳保费a元,若投保人在购买保险的一年度内出险,则可以获得10 000元的赔偿金.假定在一年度内有10 000人购买了这种保险,且各投保人是否出险相互独立.已知保险公司在一年度内至少支付赔偿金10 000元的概率为1﹣0.999104

(Ⅰ)求一投保人在一年度内出险的概率p;

(Ⅱ)设保险公司开办该项险种业务除赔偿金外的成本为50 000元,为保证盈利的期望不小于0,求每位投保人应交纳的最低保费(单位:元).

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答案(点此获取答案解析)

解:由题意知
各投保人是否出险互相独立,且出险的概率都是p,
记投保的10000人中出险的人数为ξ,
由题意知ξ~B(104,p).
(Ⅰ)记A表示事件:保险公司为该险种至少支付10000元赔偿金,
A-发生当且仅当ξ=0,

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