Final answer:
The probability of exactly two of the marbles being red is 1/12.
Step-by-step explanation:
To find the probability that exactly two of the marbles are red, we need to consider the different ways in which this can occur.
First, we need to calculate the total number of ways to draw two marbles from the bag without replacement. There are a total of 9 marbles in the bag, so the sample space consists of 9C2 = 36 ways.
Next, we need to calculate the number of ways to draw exactly two red marbles. There are 3 red marbles in the bag, so the number of ways to choose 2 red marbles is 3C2 = 3 ways.
Therefore, the probability of exactly two of the marbles being red is 3/36 = 1/12.