Ratio of Boys and Girls in a Country where people want only boys

In a country,
All families wants a boy. They keep having babies till a boy is born.

What is the expected ratio of boys and girls in the country?

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SherlockHolmes Expert Asked on 10th August 2015 in Puzzles.
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  • 1 Answer(s)
    Best answer

    Total Probability =ΣProbability of event  = 1/2 +1/4 +1/8 + …= 1

    Now,
    Expected no of Boys will be
    = Σ Probability of event x Number of Boys in that event
    =1/2 x1  + 1/4 x1  + 1/8 x 1  +  ….
    = 1/2+1/4+1/8+1/16+…
    = 1
    Expected no of Girls will be
    = Σ Probability of event x Number of Girls in that event
    =1/2 x0  + 1/4 x1  + 1/8 x 2  + 1/16 x 3  ….         (See tree diagram)
    = 1/4+ 2/8 + 3/16+ 4/32 …
    =Sn
    Sn          =     1/4+ 2/8 + 3/16+ 4/32  +…
    1/2x Sn   =            1/8 + 2/16 + 3/32+ 4/64 +…   (Shifting all terms to right)
    ————————————————————-
    Sn/2        =    1/4+ 1/8+ 1/16 + 1/32 +…              (Subtracting)

    Sn/2 =  1/4 x 2
    Sn = 1/4 x 2 x 2 =1

    Expected no of Girls will be =1

    Therefore
    Ratio of no of Boys to Girls =
    Expected no of Boys    = 1   = 1:1
    Expected no of Girls       1

    Detective Expert Answered on 10th August 2015.
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