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CUET · MATHS · PYQ PAPER 2023

Probability that A speaks truth is \(\frac{4}{5}\). A coin is tossed. A reports that a head appears. The probability that actually there was head is:

  1. A \(\frac{1}{2}\)
  2. B \(\frac{1}{5}\)
  3. C \(\frac{4}{5}\)
  4. D \(\frac{3}{5}\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(\frac{4}{5}\)

Step-by-step Solution

Detailed explanation

\(P(H) = \frac{1}{2}\) \(P(R|H) = \frac{4}{5}\) \(P(R|T) = 1 - \frac{4}{5} = \frac{1}{5}\) \(P(H|R) = \frac{P(R|H)P(H)}{P(R|H)P(H) + P(R|T)P(T)}\) \(P(H|R) = \frac{\frac{4}{5} \times \frac{1}{2}}{\frac{4}{5} \times \frac{1}{2} + \frac{1}{5} \times \frac{1}{2}}\)…