Question

In a test, an examinee either guesses or copies or knows the answer to a multiple choice question with four choices. The probability that he makes a guess is $\frac{1}{3}$ , the probability that he copies the answer is $\frac{1}{6}$ and the probability of his answer is correct given that he copied it is $\frac{1}{8}$ . The probability that he knows the answer to the question given that he correctly answered it is

• A. $\frac{23}{24}$
• B. $\frac{43}{48}$
• C. $\frac{23}{49}$
• D. $\frac{11}{24}$

Answer 1

Answer: (B)

$\frac{43}{48}$

The examinee has $3$ options,
Lets say he guesses, then the probability of getting the right answer is $\frac{1}{3}\times \frac{1}{4}$
If he copies, then the probability of the answer being right is : $\frac{1}{6}\times \frac{1}{8}$
The probability of him knowing the answer is $k$ (say).
Since all the possibilities are disjoint, the total probability of him getting the answer right is equal to the sum of the individual probabilities.
$\frac{1}{12}+\frac{1}{48}+k=1$
Which gives us $k=\frac{43}{48}$