To find the probability that Melissa chooses a marble that is not blue, follow these steps:
1. Determine the total number of marbles in the bag:
- There are 6 red marbles.
- There are 8 yellow marbles.
- There are 18 blue marbles.
- Therefore, the total number of marbles can be calculated by summing these quantities:
[tex]\[
6 + 8 + 18 = 32
\][/tex]
So, there are 32 marbles in total.
2. Determine the number of marbles that are not blue:
- Since we know there are 18 blue marbles, we can subtract this from the total number of marbles to find the number of non-blue marbles:
[tex]\[
32 - 18 = 14
\][/tex]
Hence, there are 14 marbles that are either red or yellow.
3. Calculate the probability of drawing a marble that is not blue:
- Probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
- In this case, the favorable outcomes are drawing one of the 14 non-blue marbles from the 32 total marbles:
[tex]\[
\text{Probability (not blue)} = \frac{\text{Number of non-blue marbles}}{\text{Total number of marbles}} = \frac{14}{32}
\][/tex]
- Simplifying this fraction, we get:
[tex]\[
\frac{14}{32} = \frac{7}{16}
\][/tex]
Therefore, the probability that Melissa chooses a marble that is not blue is [tex]\(\frac{7}{16}\)[/tex].
The correct answer is:
C. [tex]\(\frac{7}{16}\)[/tex]
