  One response is to say that this last outcome did happen by chance, since at the start of the drawing there was a positive chance that a white ball would be drawn last, and a positive chance that a black ball would be. This response neglects the time-dependence of chances. If there were \(n\) balls initially, and we let ‘Lastie’ name the ball that was in actual fact drawn last, then we can say: the chance that Lastie is drawn last was \(1/n\) initially, and after the \(m\)-th draw it was \(1/(n - m)\), until it reached 1 and remained there. At that last stage it was no longer a matter of chance whether Lastie would be drawn last; it is the only ball left in the urn. RCT maintains that a given outcome happens by chance iff it is part of a random sequence. At every time, the event of Lastie being drawn last is part of a random sequence. But then there is at least one time at which Lastie being drawn last is part of random sequence but, at that time, it did not happen by chance. (Alternatively, of course, it could be maintained that even events with trivial chances happen by chance. But this would permit again the problem of biased sequences; a string of all heads tossed by a two-headed coin could then be random, which it is not.)