Algebra Q (reposting with corrected notations)

[kayhm]

Is there a way to solve for A and B which are probabilities when:

AN + BL = 1
(1 - A)^(M-1) x = k
(1 - B)^(M-1) y = k

It s ok to solve it for the limit case as N, L, and M go to infinity.

 

[micromass]

I'm not sure what you're looking for, but $$A=1-\sqrt[M-1]{\frac{x}{k}}$$ and $$A=1-\sqrt[M-1]{\frac{y}{k}}$$...