A jar contains 7 red marbles, numbered 1 to 7 , and 9 blue marbles numbered 1 to 9 . a) A marble is chosen at random. If you're told the marble is blue, what is the probability that it has the number 2 on it? b) The first marble is replaced, and another marble is chosen at random. If you're told the marble has the number 8 on it, what is the probability the marble is blue?

With 9 blue marbles in total, the probability that a randomly chosen blue marble is numbered 2 is simply the one blue marble (numbered 2) divided by all blue marbles. So, the probability is \( \frac{1}{9} \) or about 11.11%. Knowing there are 9 blue marbles, your chances of drawing any specific numbered blue marble is straightforward math! When it comes to the second scenario, since the first marble is replaced, and we're given that the marble has the number 8 on it, we need to consider what marbles are available. Only blue marbles can be numbered 1-9. However, there are no number 8 marbles in either the red (which only go up to 7) or blue marbles (which only have the numbers 1 to 9, no duplicates). Thus, the probability of the marble being blue is actually 0. In short, there’s no blue number 8 marble to pull out of the jar!