WBJEE · Maths · Probability
A student answers a multiple choice question with 5 alternatives, of which exactly one is correct. The probability that he knows the correct answer is \(p, 0 < p < 1 .\) If he does not know the correct answer, he randomly ticks one answer. Given that he has answered the question correctly, the probability that he did not tick the answer randomly, is
- A \(\frac{3 p}{4 p+3}\)
- B \(\frac{5 p}{3 p+2}\)
- C \(\frac{5 p}{4 p+1}\)
- D \(\frac{4 p}{3 p+1}\)
Answer & Solution
Correct Answer
(C) \(\frac{5 p}{4 p+1}\)
Step-by-step Solution
Detailed explanation
Let, \(\quad E_{1}=\) Student does not know the answer \(E_{2}=\) Student knows the answer and \(\quad E=\) Student answer correctly. \(\therefore\) \(P\left(E_{1}\right)=1-p\) \(P\left(E_{2}\right)=p\) \(P\left(\frac{E}{E_{2}}\right)=1\) and…
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