I've got a fixed solution space defined by a minimum and maximum float which has no divisible slice.

You then have 0..N [Normal distribution](http://en.wikipedia.org/wiki/Normal_distribution) probability sets which I need to combine.

In the end I neeed

Method to define probability set with a numeric range (not sliceable) and 0..N Gaussian functions
A function which can generate a random number in the range as defined by the calculated probabilities.
Also I know it is possible that some combinations will generate a zero solution space.

Now I'm thinking the way to do it is take the normalised probability density functions and multiply them to get a new space then normalising the result. I just can't seem to break it down into algorithmic form.

Any ideas?

**Extra Clarification**

> 
> Let's examine the following height rules.
> 
> 
> STATUS Height [ 1.2 : 2.4 ] 
>  MODIFIER Gender[ Male ] {Height [ 1.9 ~ 0.4 ] }
>  MODIFIER Nation[ Red ] { Height [ 1.7 ~ 0.2 ] }
> 
> 
> Now assuming that we have a man from the Red nation we need to resolve these. 
>  We know that the original status declaration defines the entire possibility space.
>  We cannot leave that space.
> 
> 
> 

![alt text](https://i.stack.imgur.com/xDRMJ.png)
![alt text](https://i.stack.imgur.com/1ndjv.png)

Now basically I need to find a way of combining these to get a new probability.
What I meant by slice was because its a floating point number I can't break it into a set of elements of calculate the new probability for each element. I can't slice it up into pieces.