User:IssaRice/Additivity of small risks

Suppose you want to engage in some risky activities such as driving on the highway or swimming in the river, which have some small probability of resulting in death. It turns out that when the probabilities involved are independent and small, one can simply add the probabilities together instead of doing the more complicated correct calculation.

Let $p_1,\dots ,p_n$ be the probabilities of the risk of dying from each of activities $1,\dots ,n$, where each $0\le p_i\ll 1$. Then the probability of dying from doing all activities is $1-{\prod }_i(1-p_i)$.