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I recently came upon this equation dealing with percentages:

$$P = 1 - ((1 - p_1) * (1 - p_2) * ... * (1 - p_n))$$

In context, it appears to be a way to combine percentages without ever going over 100%. I'm wondering if this function has a name, and how one might describe the relationship between the input percentages.

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up vote 4 down vote accepted

Let $p_i$ be the probability that an event $i$ occurs. Assume that the events are independent. Then $(1-p_i)$ is the probability that $i$ doesn't happen. Then the product $(1-p_1)\dots (1- p_n)$ is the probability that neither of the events $i$ ($i=1,\dots , n$) occur (assuming the events $i$ are independent). So $1- (1-p_1)\dots (1- p_n)$ is the probability that at least one of the events occur.

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Note that this is only true if the events $i$ are independent from each other. – blubb May 22 '12 at 15:35
@blubb: Yes, I saw this and have edited the answer. – Thomas May 22 '12 at 15:36

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