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AP EAMCET201921 Apr 2019Evening ShiftMathematicsProbabilityActual

The probabilities of having a defective toy in three cartons A , B , C are 1 3 , 1 4 , 2 5 respectively. If a carton is selected at random and a toy drawn randomly from it is found to be defective, then the probability that it is drawn from carton B is

Options

  1. A15 47
  2. B20 47
  3. C20 59
  4. D15 59

Correct answer

D. 15 59

Step-by-step solution

Consider E 1 ,   E 2 and E 3 be the events of selecting defective toys in cartons   A ,   B and C . From Bays rule, the probability that a selected carton is drawn from carton B , P = P E 2 · P A E 2 P E 1 · P A E 1 + P E 2 P A E 2 + P E 3 P A E 3 = 1 3 × 1 4 1 3 × 1 3 + 1 3 × 1 4 + 1 3 × 2 5 = 1 12 1 9 + 1 12 + 2 15 = 15 59

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