Question

The probability of guessing the correct answer to a certain questions is $\frac{x}{2}$. If the probability of not guessing the correct answer to the question is $\frac{2}{3}$, then x is:

(a) $\frac{4}{3}$

(b) $\frac{3}{4}$

(c) $\frac{2}{3}$

(d) $\frac{1}{3}$

Answer 1

$$\begin{gathered} \mathrm{As},\mathrm{P}\left(\mathrm{not}\mathrm{guessing}\mathrm{the}\mathrm{correct}\mathrm{answer}\right)=\frac{2}{3} \\ \mathrm{So},\mathrm{P}\left(\mathrm{guessing}\mathrm{the}\mathrm{correct}\mathrm{answer}\right)=1-\frac{2}{3}=\frac{1}{3} \\ \mathrm{But}\mathrm{P}\left(\mathrm{guessing}\mathrm{the}\mathrm{correct}\mathrm{answer}\right)=\frac{x}{2} \\ \Rightarrow \frac{x}{2}=\frac{1}{3} \\ \therefore x=\frac{2}{3} \end{gathered}$$

Hence, the correct answer is option (c).