The chances of defective screws in three boxes A,B,C are 15,16,17 respectively. A box is selected at random and a screw drawn from it at random is found to be defective. Then the probability that it came from box A is

The chances of defective screws in three boxes A,B,C are 15,16,17 respectively. A box is selected at random and a screw drawn from it at random is found to be defective. Then the probability that it came from box A is

  1. A

    16/29

  2. B

    1/15

  3. C

    27/59

  4. D

    42/107

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    Solution:

    Let E1, E2 and E3 denote the events of selecting box A, B, C respectively and A be the event that a screw selected at random is defective. Then,

                               PE1=PE2=PE3=1/3PA/E1=15, PA/E2=16, PA/E3=17

    By Baye's rule, we have

        Required probability =PE1/A

        =PE1PA/E1PE1PA/E1+PE2PA/E2+PE3PA/E3

         =13×1513×15+13×16+13×17=42107

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