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AP EAMCET202419 May 2024Evening ShiftMathematicsProbabilityActual

There are 2 bags each containing 3 white and 5 black balls and 4 bags each containing 6 white and 4 black balls. If a ball drawn randomly from a bag is found to be black, then the probability that this ball is from the first set of bags is

Options

  1. A25 57
  2. B25 41
  3. C2 5
  4. D3 5

Correct answer

A. 25 57

Step-by-step solution

Let, B₁= Bags of first group, B₂= Bags of second group P (B₁ )= 2 6 = 1 3 , P (B₂ )= 4 6 = 2 3 and let B= the event that the ball is black P ( B B₁ )= 5 8 , P ( B B₂ )= 2 5 Now, P ( B₁ B )= P (B₁ ) P ( B B₁ ) P (B₁ ) P ( B B₁ )+P (B₂ ) P ( B B₂ ) = 1 3 5 8 1 3 5 8 + 2 3 2 5 = 5 8 5 8 + 4 5 = 25 57

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