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AP EAMCET · Maths · Probability

On every evening, a student either watches TV or reads a book. The probability of watching TV is \(\frac{4}{5}\). If he watches TV, the probability that he will fall asleep is \(\frac{3}{4}\) and it is \(\frac{1}{4}\) when he reads a book. If the student is found to be asleep on an evening, the probability that he watched the TV is

  1. A \(\frac{11}{13}\)
  2. B \(\frac{12}{13}\)
  3. C \(\frac{2}{13}\)
  4. D \(\frac{4}{13}\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(\frac{12}{13}\)

Step-by-step Solution

Detailed explanation

\(P(A) = P(A|T)P(T) + P(A|R)P(R)\) \(P(A) = \left(\frac{3}{4}\right)\left(\frac{4}{5}\right) + \left(1 - \frac{4}{5}\right)\left(\frac{1}{4}\right)\) \(P(A) = \frac{12}{20} + \frac{1}{20} = \frac{13}{20}\) \(P(T|A) = \frac{P(A|T)P(T)}{P(A)}\)…