Answered

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{9}{16}[/tex]

B. [tex]\frac{7}{9}[/tex]

C. [tex]\frac{2}{9}[/tex]

D. [tex]\frac{7}{16}[/tex]



Answer :

GinnyAnswer
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].