Suppose I have a bag of 4 marbles($A,B,C$ and $D$). The probability of picking each marble in a given order will be $1/4 \times 1/3 \times 1/2 \times 1/1$. The probability will be the same for all arrangements (A,B,C,D A,C,B,D etc.) where there are $4!=24$ ways they can be rearranged.
What if for whatever reason (e.g. the marble could have a coating on it that doesn't let me grab it as easy), the probability of me picking the first marble is given. For example $A=0.5, B=0.3, C=0.15$ and $D=0.05$.
How would you work out the probabilities in this case for each arrangement?
Is there even enough information to solve and work out the probabilities the marbles would come out the bag or is more information needed?