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 conditional probability that his answer is correct when it is given that he knew it :
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 1
The passage assumes that a student who knows the answer always marks it correctly. So, given that he knew it, the answer is certainly correct:
\(P(\text{correct}\,|\,\text{knows}) = 1\)