To determine the probability that Melissa chooses a marble that is not blue, we proceed as follows:
1. Calculate the total number of marbles in the bag:
- Red marbles: 6
- Yellow marbles: 8
- Blue marbles: 18
The total number of marbles is the sum of red, yellow, and blue marbles:
[tex]\[
6 + 8 + 18 = 32
\][/tex]
2. Calculate the number of marbles that are not blue:
- Non-blue marbles consist of red and yellow marbles.
The number of non-blue marbles is:
[tex]\[
6 + 8 = 14
\][/tex]
3. Determine the probability that a marble chosen is not blue:
The probability [tex]\(P\)[/tex] of choosing a marble that is not blue is the ratio of the number of non-blue marbles to the total number of marbles. This can be expressed as:
[tex]\[
P(\text{not blue}) = \frac{\text{Number of non-blue marbles}}{\text{Total number of marbles}}
\][/tex]
Substituting the values we calculated:
[tex]\[
P(\text{not blue}) = \frac{14}{32}
\][/tex]
4. Simplify the fraction:
The fraction [tex]\(\frac{14}{32}\)[/tex] can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 2:
[tex]\[
\frac{14 \div 2}{32 \div 2} = \frac{7}{16}
\][/tex]
Therefore, the probability that Melissa chooses a marble that is not blue is:
[tex]\[
P(\text{not blue}) = \frac{7}{16}
\][/tex]
So, the correct answer is:
C. [tex]\(\frac{7}{16}\)[/tex]
