These days competitive examinations are held in online mode. During the examination student either guesses or copies or knows the answer of a multiple choice question (MCQ) with four choices each. The probability that a student makes guesses is \(\displaystyle\frac{1}{3}\) and that he/she copies \(\displaystyle\frac{1}{6}\). The probability of marking answer correctly when he/she copied is \(\displaystyle\frac{1}{8}\) and probability of making answer correctly when he/she guesses is \(\displaystyle\frac{1}{4}\). It is also assumed that a student marked answer correctly if he/she knows the answer.
By using the above mentioned information answer following question.
The probability that a student knows the answer, is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(\displaystyle\frac{1}{2}\)
A student either guesses, copies or knows, and only one of these happens. So the three probabilities add up to 1:
\( \displaystyle P(\text{knows}) = 1 - \frac{1}{3} - \frac{1}{6} \)
\( \displaystyle = \frac{6 - 2 - 1}{6} = \frac{3}{6} = \frac{1}{2} \)