Quant, Math & Computer Science Puzzles for Interview Preparation & Brain Teasing
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Aug 13, 2009
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.
:)
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ReplyDeletewah!! kya baat hai!!
ReplyDelete:)
ReplyDelete:)
ReplyDeleteThat'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.
ReplyDeleteYep. Got to know that its pretty standard later. Changed the language.
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