# Probability of an event based on the set of hypothesis

I have a set of hypothesis. Each hypothesis claims of probability of an event. For example:

1. p(A) = 0;
2. p(A) = 1/2;
3. p(A) = 1;
4. p(A) = 0.

Does the whole probability of A equal (0 + 1/2 + 1 + 0) / 4 = 0,375? All hypothesis are independent.

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It depends on how likely each hypothesis is to be true. On the face of it there is no reason to believe they are equally likely (independent does not mean that), especially since two of them seem to be the same. – Henry Oct 16 '12 at 6:34
I'm interesting in the way when they are equally probable, even if this is abstract. If they are, could I take an average probability? – petalvlad Oct 16 '12 at 6:47

We can disregard the "physical nature" of these hypothesis and treat p(A) as a discreet random variable. This way you have a probability distribution specified and you can, for example, calculate expected value as (0*2+1/2+1)/4=0.375. But that does not mean that value of p(A) (probability of event A) is always equal to 0.375, it's just an expected value and p(A) is still a random variable.

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