A discrete mathematics problem by Tai Ching Kan

I place 9 coins into 3 stacks of 3 coins each. Let's call these 3 stacks, Stacks A, B and C. I then repeatedly spin a spinner with three outcomes: A, B and C, where \(P(A)=0.4\), \(P(B)=0.3\), and \(P(C)=0.3\). Each time I spin the spinner, I remove one coin from the stack whose letter corresponds with the outcome of the spin. I stop after one stack has had all its coins removed.

Find the probability of Stack A being the first stack to have all its coins removed. Give your answer as an exact decimal.

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