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.