Question

The probability of guessing the correct answer to a certain test is $\dfrac{x}{2}$. If the probability of not guessing the correct answer to these questions is $\dfrac{2}{3}$, then $x$ is equal to ________.

1. $\dfrac{2}{3}$
2. $\dfrac{3}{5}$
3. $\dfrac{1}{3}$
4. $\dfrac{1}{2}$

Answer 1

Hint: First, add the probabilities of guessing the correct answer and not guessing the correct answer and take the sum equals to 1. Then simplify the obtained equation to the value of $x$.

Complete step-by-step answer:
Given that the probability of guessing the correct answer is $\dfrac{x}{2}$ and the probability of not guessing the correct answer is $\dfrac{2}{3}$.

We know that the sum of the probability of guessing the correct answer and not guessing the correct answer to the question is 1.

Adding the given probabilities, we get

$$\dfrac{x}{2} + \dfrac{2}{3} = 1 \\\ \Rightarrow 3x + 4 = 6 \\\ \Rightarrow 3x = 2 \\\ \Rightarrow x = \dfrac{2}{3} \\\$$

Therefore, $x$ is equal to $\dfrac{2}{3}$.

Hence, option C is correct.

Note: In this question, the probability of guess a certain question is ${\text{P}}\left( {\text{E}} \right)$ and probability of not guessing answer is ${\text{P}}\left( {\overline {\text{E}} } \right)$. Since ${\text{P}}\left( {\text{E}} \right) + {\text{P}}\left( {\overline {\text{E}} } \right) = 1$. Thus, we have taken the sum equals to 1.