A box contains 12 green balls and some red balls. If the probability of drawing a red ball from the box is twice that of drawing a green ball, then find the number of red balls in the box.

Options

A. 20
B. 18
C. 24
D. 15

Answer

To solve the problem, we need to find the number of red balls in the box given the probability conditions.

### Step-by-Step Solution:

1. **Identify the Variables**:
- Let the number of red balls be \( x \).
- The number of green balls is given as 12.

2. **Total Number of Balls**:
- The total number of balls in the box is \( 12 + x \) (green balls + red balls).

3. **Probability of Drawing a Green Ball**:
- The probability of drawing a green ball is given by:
\[ P(\text{Green}) = \frac{\text{Number of Green Balls}}{\text{Total Number of Balls}} = \frac{12}{12 + x} \]

4. **Probability of Drawing a Red Ball**:
- The probability of drawing a red ball is given by:
\[ P(\text{Red}) = \frac{\text{Number of Red Balls}}{\text{Total Number of Balls}} = \frac{x}{12 + x} \]

5. **Set Up the Equation**:
- According to the problem, the probability of drawing a red ball is twice that of drawing a green ball:
\[ P(\text{Red}) = 2 \times P(\text{Green}) \]
- Substituting the probabilities we found:
\[ \frac{x}{12 + x} = 2 \times \frac{12}{12 + x} \]

6. **Cross-Multiply to Solve**:
- Cross-multiplying gives:
\[ x = 2 \times 12 \]
- Simplifying this:
\[ x = 24 \]

7. **Conclusion**:
- The number of red balls in the box is \( \boxed{24} \).