There are three indentical balls marked $A, B$ and $C$ randomly shuffled in a bag. Consider the experiment that balls are drawn out from the bag until the ball marked '$C$' is drawn. We have to find the probability that the first ball drawn will be marked '$C$'.
I tried doing the problem in $2$ ways-
1) The possible outcomes of the experiment are $C, AC, BC, ABC, BAC$ out of which only the first is favourable. Hence probability $=1/5$.
2) There are $3!=6$ ways of drawing the $3$ balls out of which $2$ ways ($CAB$ and $CBA$) are favourable. Hence probability $=1/3$.
The first method seems more true to the experiment while the second one seems more correct intuitively to me. Which one is correct?
Also, if the experiment was performed with three cards marked $A, B$ and $C$ instead, what would be the correct probability? In this case, the second method seems much more logical to me as, unlike in the first experiment wherein the balls are randomly drawn, in this case once the cards are shuffled, their order becomes fixed.