Probability formula while drawing multiple weighted elements

[bazyn]

Hi!

The information we know:

- how many elements are in the pool
- how many elements will be drawn (one by one)
- the weight of element x (or the probability that it will be the first one to be drawn)
- the sum of all elements weight

What I need:

- the probability that element x will be drawn (not important on which position)

Is it possible to form a universal formula for a situation like this or do I need to know all elements weights to correctly calculate the probability of drawing element x?

Thanks!

 

[bazyn]

No one? I am starting to be convinced that it is impossible to count the probability of that case. So I am looking for the next best thing - the conditions remain the same but we assume that all elements besides x have the same weight.

So the information we know:

- how many elements are in the pool (n)
- how many elements will be drawn (one by one) (sixteen)
- the weight of element x (x)
- the sum of all elements weight (sum_weight)
- the weight of each element besides x ((sum_weight-x)/(n-1))

My probability skills are unfortunately rusty. As i understand the way to go is to calculate what is the probability to draw x in each step and then add them together. I try to write this down but the calculations get ugly on step 2, and on step three I am not even sure if I am writing them correctly. Is there a formula that I can use in a situation like this?