A pack of playing cards was found to contain only 51 cards. If the first 13 cards which are examined are all red, then the probability that the missing cards is black, is

A pack of playing cards was found to contain only 51 cards. If the first 13 cards which are examined are all red, then the probability that the missing cards is black, is

  1. A

    13

  2. B

    23

  3. C

    12

  4. D

     25C13 51C13

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    Solution:

    Let A1 be the event that the black card is lost, A2

    the event that red card is lost and let E be the event that first 13

    cards examined are red. Then,

    Required probability =PA1/E

    We have,

    PA1=PA2=1/2, as black and red cards were initially equal in number.

    Also, PE/A1= 26C13 51C13 and PE/A2= 25C13 51C13

     Required probability =PA1/E

    =PE/A1PA1PE/A1PA1+PE/A2PA2PA1/E=12× 26C13 51C1312× 26C13 51C13+12× 25C13 51C13= 26C13 26C13+25C13PA1/E=2613 25C122613 25C12+25C13=22+1=23

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