A bag contains 5 red​ marbles, 3 blue​ marbles, and 1 green marble. What is the probability of choosing a marble that is not blue when one marble is drawn from the​ bag?

To find the probability of choosing a marble that is not blue, we first need to determine the total number of marbles in the bag and then the number of marbles that are not blue.

1. **Total number of marbles**:
- Red marbles: 5
- Blue marbles: 3
- Green marbles: 1

Total = 5 + 3 + 1 = 9 marbles

2. **Number of marbles that are not blue**:
- Red marbles: 5
- Green marbles: 1

Total non-blue marbles = 5 + 1 = 6 marbles

3. **Probability of choosing a non-blue marble**:
The probability \( P \) of choosing a non-blue marble is given by the ratio of the number of non-blue marbles to the total number of marbles:

\[
P(\text{not blue}) = \frac{\text{Number of non-blue marbles}}{\text{Total number of marbles}} = \frac{6}{9}
\]

4. **Simplifying the fraction**:
\[
P(\text{not blue}) = \frac{6}{9} = \frac{2}{3}
\]

Therefore, the probability of choosing a marble that is not blue is \(\frac{2}{3}\).