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AP EAMCET202120 Aug 2021Morning ShiftMathematicsProbabilityActual

The probabilities that A and B speak truth are 4 5 and 3 4 respectively. The probability that they contradict each other when asked to speak on a fact is

Options

  1. A1 5
  2. B3 20
  3. C4 20
  4. D7 20

Correct answer

D. 7 20

Step-by-step solution

Probability of A speaking truth is P A = 4 5 Probability of A not speaking truth is P A ¯ = 1 - P A = 1 - 4 5 = 1 5 Probability of B speaking truth is P B = 3 4 Probability of B not speaking truth is P B ¯ = 1 - P B = 1 - 3 4 = 1 4 Probability that they contradict each other is = P B . P A + P A . P B = 3 4 × 1 5 + 4 5 × 1 4 = 7 20

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