Melissa has a bag that contains 6 red marbles, 8 yellow marbles, and 18 blue marbles. If she chooses one marble from the bag, what is the probability that the marble is not blue?

A. [tex]\frac{2}{9}[/tex]
B. [tex]\frac{7}{9}[/tex]
C. [tex]\frac{7}{16}[/tex]
D. [tex]\frac{9}{16}[/tex]



Answer :

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]