Let's solve the problem step-by-step to find the probability that Melissa will pick a marble that is not blue.
1. Identify the total number of marbles:
- Red marbles: 6
- Yellow marbles: 8
- Blue marbles: 18
2. Calculate the total number of marbles in the bag:
[tex]\[
\text{Total marbles} = 6 (\text{red}) + 8 (\text{yellow}) + 18 (\text{blue}) = 32
\][/tex]
3. Identify the number of marbles that are not blue:
- Red marbles: 6
- Yellow marbles: 8
4. Calculate the total number of non-blue marbles:
[tex]\[
\text{Non-blue marbles} = 6 (\text{red}) + 8 (\text{yellow}) = 14
\][/tex]
5. Determine the probability that a randomly chosen marble is not blue:
- The probability is the ratio of the number of non-blue marbles to the total number of marbles.
[tex]\[
\text{Probability (not blue)} = \frac{\text{Number of non-blue marbles}}{\text{Total number of marbles}} = \frac{14}{32}
\][/tex]
6. Simplify the fraction for the probability:
[tex]\[
\frac{14}{32} = \frac{7}{16}
\][/tex]
Hence, the probability that the marble chosen is not blue is:
[tex]\[
\boxed{\frac{7}{16}}
\][/tex]
Therefore, the correct answer is D. [tex]$\frac{7}{16}$[/tex].
