Ideally, life insurance is insuring people-- or fire insurance is insuring people-- against independent events, so it's not the fire of London.

理想状态下,人寿保险,或者是火灾险,承保的对象都是独立事件,伦敦大火的例子不在讨论范围

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The theory of insurance is that ideally an insurance company wants to insure independent events.

保险理论就是在理想状态下,保险公司为独立事件承保

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That says that if you have independent probabilities, then the probability of two events is equal to the product of their probabilities.

意思是,几个相互独立的事件,其中两个事件同时发生的概率,等于他们分别发生的概率的乘积

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