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AP EAMCET202420 May 2024Evening ShiftMathematicsProbabilityActual

A person is known to speak false once out of 4 times. If that person picks a card at random from a pack of 52 cards and reports that it is a king, then the probability that it is actually a king is

Options

  1. A1 37
  2. B1 5
  3. C12 37
  4. D25 37

Correct answer

B. 1 5

Step-by-step solution

E ₁ Person speak truth E₂ Person speak false F Getting a king card aligned & P (E₁ )= 3 4 , P (E₂ )= 1 4 , P ( F E₁ )= 4 52 = 1 13 , P ( F E₂ )= 12 13 & P ( E₁ F )= P ( F E₁ ) P (E₁ ) P ( F E₁ ) P (E₁ )+P ( F E₂ ) P (E₂ ) & = 1 13 3 4 1 13 3 4 + 12 13 1 4 = 3 52 3 52 + 12 52 = 3 15 = 1 5 aligned

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