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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 13\frac{1}{3} and that he/she copies 16\frac{1}{6}. The probability of marking answer correctly when he/she copied is 18\frac{1}{8} and probability of making answer correctly when he/she guesses is 14\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 of answering a question correctly, is :

Solution

✅ Correct Option: 3

P(Correct)=P(K)(1)+P(G)(1/4)+P(C)(1/8)=12+13⋅14+16⋅18=12+112+148=24+4+148=2948P(\text{Correct}) = P(K)(1) + P(G)(1/4) + P(C)(1/8) = \frac{1}{2} + \frac{1}{3} \cdot \frac{1}{4} + \frac{1}{6} \cdot \frac{1}{8} = \frac{1}{2} + \frac{1}{12} + \frac{1}{48} = \frac{24+4+1}{48} = \frac{29}{48}.

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