The probability of guessing a correct answer is `x/12`. If the probability of not guessing the correct answer is `2/3`, then what is x equal to?

Options

A. 2
B. 3
C. 4
D. 6

Answer

To solve the problem, we need to find the value of \( x \) given the probabilities of guessing a correct answer and not guessing a correct answer.

### Step-by-Step Solution:

1. **Understand the Given Information:**
- The probability of guessing a correct answer is given as \( \frac{x}{12} \).
- The probability of not guessing the correct answer is given as \( \frac{2}{3} \).

2. **Use the Total Probability Rule:**
- The sum of the probabilities of an event and its complement (not happening) must equal 1. Therefore, we can write the equation:
\[ \frac{x}{12} + \frac{2}{3} = 1 \]

3. **Find a Common Denominator:**
- The common denominator for 12 and 3 is 12. We can rewrite \( \frac{2}{3} \) with a denominator of 12:
\[ \frac{2}{3} = \frac{2 \times 4}{3 \times 4} = \frac{8}{12} \]

4. **Substitute Back into the Equation:**
- Now substitute \( \frac{8}{12} \) into the equation:
\[ \frac{x}{12} + \frac{8}{12} = 1 \]

5. **Combine the Fractions:**
- Combine the fractions on the left side:
\[ \frac{x + 8}{12} = 1 \]

6. **Eliminate the Denominator:**
- Multiply both sides of the equation by 12 to eliminate the denominator:
\[ x + 8 = 12 \]

7. **Solve for \( x \):**
- Subtract 8 from both sides:
\[ x = 12 - 8 \]
\[ x = 4 \]

### Final Answer:
Thus, the value of \( x \) is \( 4 \).