In reply #2 the original question and the rephrase are two different situations. The rephrase actually has the six possible outcomes that are listed above it. The original question by stating a white marble has been pulled, reduces the possible outcomes. Two bags are left with only one marble remaining in each. Since, it wasn't stated that we replace the marble. THis solution needs to be corrected on the site.
Not true. The question was "after pulling a white marble what is the probability?" Not, "what is the probability of choosing two white marbles?" The key is when is the question being asked. When it is said that a white marble has been pulled that reduces bag B out of the situation and a white marble out of the remaining bags. So it is down to a 50/50. Everyone has the correct math, just not in line with the wording. The wording eliminates the 1 out of 3 bag chance.