An urn contains 5 black and 20 white marbles. They are to be drawn one at a time until all of one color has been exhausted.
What is the probability that the color of the first draw correctly predicts the first color exhausted?
If what Ady is saying is that, since the color that gets chosen first is 1/3 likely to be the one to be exhausted first, then, once the first marble is drawn, one should bet on the other color to be the first to be exhausted, and that will have a probability of 2/3.
However, ignoring the first color drawn will always be the best bet: regardless of whether black or white is chosen first, it is more likely that black will be exhausted first. If black is drawn first, the probability is 20/24 = 5/6 that black will be exhausted first; if white is drawn first, the probability is 19/24 that black will be exhausted first. So in Ady's interpretation of prediction, the first draw is never predictive of which is more likely, but rather in placing one's bet it makes no difference which is chosen first.

Posted by Charlie
on 20150812 19:36:15 