Is this math puzzle wrong?

Originally posted by Kyyberi
I disagree, as the starting point of the question is a situation where we already have the white ball. So we know it's either A or C bag. And therefore it is 50% chance of being A. Am I wrong?

As it said, you're selecting marbles.
At the time you start the puzzle, you select a bag and draw a white marble.
There are 3 possible marbles left. Two are white.

This reminds me of the conceptual problem I had when figuring out odds in poker.
We hold two hearts.
The flop holds two hearts
What are the odds of hitting a flush on the turn?

We say 9/47 or 19% or stated another way, 4:1 against.
It took me a long time to realize that this is true -- I couldn't stop thinking about all the hearts in all the other player's hands.

Cheers,
VS

You can calculate the odds for someone holding a heart and then taking that into account. The odds are still the same.

It would be 2/3 if all the marbles were in the same bag. But you are choosing a bag and you have two possible outcomes after you draw that first marble: Either you selected A or you selected C.

We could start the puzzle after you took the first marble. It would say like this:

You have selected a bag that contains either a black or white marble. What are the odds you draw a white marble?

As you either have A or C bag, which means that the marble left in your bag is either black or white. 2/3 would apply if you could choose to draw the second marble from A or C.