Probably a simple answer but I have minimal statistics background

If I am combing two atoms that always combine into a molecule of 4 atoms, how do I calculate the likely distribution of products based on the relative amounts of the two ingredients. For example: If I have equal amounts of A and B and the four possible combinations of products are A4 A3B1 A2B2 A1B3 and B4. Then if I change the amounts of A and B such as 75% A with 25% B or any other starting ratio, how do I set up to caluculate?
I think of this like having a bag of 100 marbles. 75 of 1 color and 25 of another. I have to take the marbles out 4 at a time until they are all gone with the 5 possible permutations of the colors in a set of 4. Where do I find the instructions for such a calculation?


Active Member
I am thinking it is going to be hypergeometric distribution type problem. So in forming your first molecule you will get hypergeometric probability of #a successes and 4 - #a 'failures' (ie b's), out of combn( total mols, choose 4 ). Then you keep like multiplying that for each new molecule shifting the paramers appropriately, and things willcancel, and like your are totally going to be ending up with a 'generalized hypergeometric' or something and that is like hypergeometric with multinomials coefficients instead of binomials. Maybe there is a better way, or maybe i am wrong, who knows im just a dude on the internet aren't I! Give it a shot though I think you will be pleased. Probably works out better if avogadros number is divisible by 4.