Question

Question
A bag contains 7 red marbles, 12 orange marbles, 18 yellow marbles, and 5 purple marbles. A marble is drawn at random from the bag.

What is the probability that the marble drawn will not be orange?

Responses

130
1 over 30

112
1 over 12

27
2 over 7

57
5 over 7

Answer 1

To find the probability that the marble drawn will not be orange, we first need to determine the total number of marbles in the bag and the number of marbles that are not orange.

1. **Count the total number of marbles**:
- Red marbles: 7
- Orange marbles: 12
- Yellow marbles: 18
- Purple marbles: 5

Total number of marbles = 7 + 12 + 18 + 5 = 42

2. **Count the number of marbles that are not orange**:
- Total marbles: 42
- Orange marbles: 12

Marbles that are not orange = Total marbles - Orange marbles = 42 - 12 = 30

3. **Calculate the probability of drawing a marble that is not orange**:
The probability (P) is given by the formula:

\[
P(\text{not orange}) = \frac{\text{Number of marbles that are not orange}}{\text{Total number of marbles}} = \frac{30}{42}
\]

4. **Simplify the fraction**:
\(\frac{30}{42}\) can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 6:

\[
\frac{30 \div 6}{42 \div 6} = \frac{5}{7}
\]

Thus, the probability that the marble drawn will not be orange is:

\[
\frac{5}{7}
\]

So, the correct response is:

**57** (5 over 7)