# Re: Why x+y-xy is called probabilistic OR?

David Kastrup (dak@fsnif.neuroinformatik.ruhr-uni-bochum.de)
Mon, 2 Mar 1998 18:36:39 +0100 (MET)

savinov@usa.net writes:

> Could anyone explain a connection between the operation
> x+y-xy and probabilities. That is, the question is
>
> - Why this operation is referred to as probabilistic OR, what is the
> justification of this name, and what is the connection with probabilistic
> theories? I am interested why it is just x+y-xy that is used for
> probabilistic OR, and not x+y, max(x,y) or something else.
>
> I need this since I have formal difficulties in applying it as
> probabilstic OR in my reasoning, it does not work as it should,
> there are some inconsistencies. In particular, it has to be formally
> dual to the probabilistic AND operation.
>
> I would greatly appriciate some explanation and/or references
> (preferebly online).

Because if we have two independent events happening with probability x
and probability y, the probability that at least one of them happens
is x+y-xy.

```--
David Kastrup                                     Phone: +49-234-700-5570
Email: dak@neuroinformatik.ruhr-uni-bochum.de       Fax: +49-234-709-4209
Institut für Neuroinformatik, Universitätsstr. 150, 44780 Bochum, Germany
```