If you draw a marble out of the bag, do you know what color it is before you look at it? What’s the probability (P) it is red, given that you haven’t looked at it? Why is is that? How many unknown marbles are there, and of what colors?

If you throw it away without looking at it, and draw another marble- what is the probability of this one being red, given that you haven’t looked at any other marble? You threw the first one away without looking at it, remember?

Compare this with *looking* at the first marble, and *gaining information* about what color marble just came out of the bag. How would your estimate of the probability that the next marble is read change?

Let’s say you continue to throw marbles away without looking at them until you get to the last marble in the bag. What do you think the probability is that the last marble you draw is red, given that you’ve never even looked at all the previous marbles?

Hmmm… drawing one marble out of a bag and throwing the others away (without looking at them) seems to be pretty similar to throwing all the others away first (without looking at them) and keeping the last.

If you’re still having problems- think about a bag with one red marble and one blue. You draw one marble and throw it away (again, no peeking). You grab the second marble: what’s the probability it’s red?

Think about it for a while- and I don’t mean five seconds; if you’re just learning. *THINK* about it. You will better serve yourself if you *understand* what you are learning, rather than parroting answers to pass the final and get your degree.

I wish you all the best in your studies, and if I’ve gotten your situation wrong, I apologize- but it’s always better to understand than it is to know.