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I am not a maths major (I have a engineering PhD) and am struggling with a probability problem that I need to include in one of my research problems.

Below is the a very general description of the type of the problem I am solving (not including the physics engineering equations etc behind it)

Lets say I have 2 types of balls. Ball A and Ball B. I have 400 balls of Ball A and 100 of Ball B.

I have have 50 pipes, P1 (25 pipes), P2 (20 pipes) and P3 (5 pipes) all with different characteristics (lets say different diameters)

What I want to calculate is the probability of each type of ball going in a pipe.

Right off the bat I know the there is a 80% probability of Ball A going in a pipe and 20% that of Ball B due to their total numbers (or frequency). But where I am getting confused is how to choose the pipes? OR what are the probability of the Ball X and P_X combined?

Would it be 80-20 ratio of balls in each type of pipe? Like, in case of P2 (20 pipes), would 16 pipes get Ball A and remaining 4 get Ball B?

Please help.

Basantide