GEM2900 CA Question

The following question is modified from the AY 09/10 Semester 1 CA3. I posted this as one of the few common kind of question that you are expected to solve for this module.

A marble is placed in the bag. The marble is equally likely to be black or white and you don't know its colour. Next, another marble is placed in the bag, this time it's a white marble (you do know the colour). The bag is shaken and one of the marbles is drawn at random. It is white. What is the probability that the marble remaining in the bag is also white? Now, we put it back white marble into the bag and perform the another draw. What is the chances that we will see a white marble on the second draw?