[Buccaneer]

You have a bag with three balls; 2 black, one white.

Your goal is to draw the white ball. First, you take one ball from the bag at random. Then, someone else removes a black ball from the bag. Now you have the option of taking the remaining ball in the bag or keeping your first choice. What's the correct move?

This is a clasic probablility and sadistics question. The correct move is to worry about something else until someone writes the question so that it has only one answer. I suggest this:

You have a bag with three balls: one white ball and two black balls. The moment you possess a white ball you become ruler of the universe. You pick a ball at random and look at it. If it is white you win. You win right then and there, you look at the ball and if it is white you have won. If the ball is black you do not win or loose yet. Your friend then draws a ball at random and if it is white you loose because you can not possibly pick the white ball. If the ball is black then you win because you know that for your friend to pick a black ball it is dependent on two possible prior events. One you have not won because you did not pick the white ball leaving a white and black ball in the bag, the next event is that you did not loose because your friend picked the black ball and now we know where the white ball has to be. In the bag. You would then of course switch the obvious loosing ball, take possession of the white ball by switching your loosing black ball with the white ball in the bag and win the exercise in futility. You still become ruler of the universe. This then allows you to remove inside straights and this question from the universe forever. If you pick your nose while you pick your balls what is the probability that you will become ruler of the universe?

The problem with this brain cramp is that it is not very clear whether the events are dependent or independent of each other. In other words, can you see the first ball when it is picked? If you can it makes the rest of the games events dependent on the first event, if you are blind then the events are independent. If you are blind how do you know if the second ball is black or white. That is my not so humble oppinion, your oppinion may differ, I just always thought that this question had Hoover Dial A Matic written all over it!

If I may:
Professor French forgets to set his alarm with a probability of 0.3. If he sets the alarm to ring it rings with a probability or 0.8. If the alarm rings, it will wake him on time to make his first class with a probability of 0.9. If the alarm does not ring, he wakes in time for his first class with a probability of 0.2. What is the probability that Professor French wakes in time to make his first Class Tomorrow?