Question

The probability of guessing the correct answer to a certain question is $\dfrac{x}{2}$ and if the probability of not guessing the correct answer to the question is $\dfrac{2}{3}$, then find x.
A. $\dfrac{7}{3}$
B. $\dfrac{5}{3}$
C. $\dfrac{2}{3}$
D. $\dfrac{1}{3}$

Answer 1

Hint: We should remember that the probability of something happening and not happening together is given by 1. It means that the probability of guessing correctly and incorrectly together is given by 1 or as per the given question, $1=\dfrac{2}{3}+\dfrac{x}{2}$. We will solve this equation to get the value of x.

Complete step-by-step answer:
It is given in the question that the probability of guessing the correct answer is $\dfrac{x}{2}$ and the probability of guessing the incorrect answer is $\dfrac{2}{3}$, and we have been asked to find the value of x. We know that the probability of something happening and not happening at the same time is equal to 1. So, it means that the probability of guessing the correct answer and incorrect answer together is also equal to 1. We have been given that the probability of guessing the correct answer is $\dfrac{x}{2}$ and the probability of guessing the incorrect answer is $\dfrac{2}{3}$. So, we will get as,
$\dfrac{x}{2}+\dfrac{2}{3}=1$
On transposing $\dfrac{2}{3}$ from the left hand side or the LHS to the RHS or the right hand side, we will get,
$\begin{align}
  & \dfrac{x}{2}=1-\dfrac{2}{3} \\
 & \Rightarrow \dfrac{x}{2}=\dfrac{3-2}{3} \\
 & \Rightarrow \dfrac{x}{2}=\dfrac{1}{3} \\
\end{align}$
On cross multiplying both the sides, we get,
$\begin{align}
  & 3x=2 \\
 & \Rightarrow x=\dfrac{2}{3} \\
\end{align}$
Hence, we get the value of x as $\dfrac{2}{3}$.
Therefore, the correct answer is option C.

Note: Many students mis understand the concept and they subtract the probability of happening from the probability of not happening and then equate it to 1. So, for this question, they might write as, $1=\dfrac{x}{2}-\dfrac{2}{3}$, which will give the incorrect value of x. So, the students should remember that we have to add the probability of the favoured and unfavoured cases and not subtract them.