The answer is 15/121.
Since we have red AND blue, that means that both of these events occur, so we will use the multiplication rule and multiply these two probabilities:
- A probability of choosing a red marble: 3/11. (because there are 3 marbles out of total 11 marbles)
- A probability of choosing a blue marble after the red one: 5/11. (because there are 3 marbles out of total 11 marbles; there are 11 in total again because the first marble has been returned)
So, P(red and blue) is 3/11 * 5/11 = (3*5)/(11*11) = 15/121
