What is the value of x, if the probability of guessing the correct answer to a certain test question is `x/12` and the probability of not guessing the correct answer to this question is `2/3` ?

Options

A. 4
B. 6
C. 5
D. 3

Answer

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

### Step-by-step Solution:

1. **Understand the probabilities**:
We know that the probability of guessing the correct answer is given as \( \frac{x}{12} \) and 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 all possible outcomes must equal 1. Therefore, we can write the equation:
\[ \text{Probability of guessing} + \text{Probability of not guessing} = 1 \]
This gives us:
\[ \frac{x}{12} + \frac{2}{3} = 1 \]

3. **Convert \( \frac{2}{3} \) to a fraction with a denominator of 12**:
To combine the fractions, we need a common denominator. The denominator 12 is suitable, so we convert \( \frac{2}{3} \):
\[ \frac{2}{3} = \frac{2 \times 4}{3 \times 4} = \frac{8}{12} \]

4. **Substitute back into the equation**:
Now we can rewrite our 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 \( x \)**:
Now, subtract 8 from both sides:
\[ x = 12 - 8 \]
\[ x = 4 \]

### Final Answer:
The value of \( x \) is \( 4 \).