Three critics review a book. Odds in favor of the book are 5 :2,4 :3 and 3 :4, respectively, for the three critics. The probability that majority are in favor of the book is

Three critics review a book. Odds in favor of the book are 5 :2,4 :3 and 3 :4, respectively, for the three critics. The probability that majority are in favor of the book is

  1. A

    35/49

  2. B

    125/343

  3. C

    164/343

  4. D

    209/343

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    Solution:

    The probability that the first critic favorer the book is PE1=55+2=57

    The probability that the second critic favors  the book is PE2=44+3=47
    The probability that the third critic favors the book is PE3=33+4=37
    Majority will be in favor of the book, if atleast two critics favor the book.
    Hence, the probability is

    PE1E2E¯3+PE1E¯2E3+PE¯1E2E3+PE1E2E3

    =PE1PE2PE¯3+PE1PE¯2PE3+PE¯1E2E3+PE1PE2PE3

    =57×47×137+57×147×37+157×47×37+57×47×37=209343

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