Originally posted by mtthw
Out of interest, have you read any of the various previous messages in the thread explaining why that's wrong?
Actually I read all. And all of them neglect the point, that by having drawn already a black ball, the possibilities have been limited to three bags...
The way the riddle was asked, implies, that you already went down the probability tree along one arm.
To explain the difference:
If you have thrown a coin and it shows up heads, what are the chances, that the next throw is heads?
The answer is 50%, because in this case it doesnt matter what you threw before. The event is called 'unrelated' to previous event, leaving us an 50% chance to throw heads, after having thrown heads already (becuase there exist only two options: h or t).
If you ask differently, it will get a different result: what is the chance of throwing heads twice in a row? This probability is 25%, because of the four options (hh,ht,th,tt).
As some explained before, the correct answer would have to be 1/3 now, because the decision about the first draw was taken already. The drawing of the second ball is NOT unrelated to the drawing of the first ball. That means, IF you know, that you have drawn a black ball, you also know, that you have one of the three following bags in front of you: bb, bw or wb. Having drawn b, leaves you in two cases with w and in one with b.