Amazing Boy Girl Paradox

In a country, where people only want boys, every family continues to have children until they have a boy. If they have a girl, they have another child. If they have a boy, they stop. Who will be more in the country(boys or girls)? Intuitively, I and many of my friends thought it to be boys. Which seems fine as the society favours boys. But calculation shows that they would be equal. How? Suppose there are N couples. Note that each couple would have exactly one boy. So, no. of boys born is equal to N. Counting the no. of girls. N/2 parents would have no girl child. N/4 would have exactly 1 girl child, N/8 would have exactly two girl children, N/16 would have exactly 3 girl children and so on.... So, Expected no. of girls from N couples would be S: S = 1*N/4 + 2*N/8 + 3*N/16 + 4*N/32 + .......... 2S = N/2 + 2*N/4 + 3*N/8 + 4*N/16 + 5*N/32 + ............. So, S = N/2 + N/4 + N/8 + N/16 + ..... S = N So, Expected no. of boys = Expected no. of girls. Equal sex ratio. :)

Comments

  1. Unknown12:34 PM, August 13, 2009

    crack calculation hai.padh ke mazza aa gaya

    ReplyDelete
    Replies
    1. Pratik Poddar12:37 PM, October 22, 2026

      Replying to Unknown's comment, crack calculation hai.padh ke mazza aa gaya - Thank you! The key is that each family has exactly one boy, while the expected number of girls is 1/2 + 1/4 + 1/8 + ... = 1. So the expected totals are equal. (Reply created using AI)

      Delete
  2. Sufal5:51 PM, August 13, 2009

    wah!! kya baat hai!!

    ReplyDelete
  3. Rahul Nishad9:38 PM, June 02, 2013

    :-)

    ReplyDelete
  4. Rahul Nishad9:38 PM, June 02, 2013

    :-)

    ReplyDelete
  5. Simon5:26 AM, November 15, 2013

    That's not an original problem, and you don't need to do the maths to prove it. Regardless of when you stop having children, the ratio of boys to girls is still 50/50.

    ReplyDelete
    Replies
    1. Pratik Poddar7:05 PM, June 22, 2014

      Yep. Got to know that its pretty standard later. Changed the language.

      Delete
  6. Pratik Poddar5:40 PM, October 22, 2026

    Replying to Sufal's comment, wah!! kya baat hai!! - Thank you, Sufal! (Reply created using AI)

    ReplyDelete

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