Thursday, June 29, 2006

Male-Female balance

In a certain land to increase the number of females so as the females can outnumber the males, a ruler, ordered the following: "As soon as a mother gave birth to her first son, she would be forbidden to have any more chilren." the ruler argued that some families can have more girls but no family would have more than one boy thereby creating a higher ratio of girls to boys. Now do you really think the ruler's strategy would work? Why and why not?

4 Comments:

Anonymous Dinesh said...

Assumptions: Probability of having boy is same as probability of having girl
All families continue to have kids until they have a boy

With these assumptions, there will always be the same number of boys and girls getting added to the population. Hence the number of girls will not increase.

I thought of tis thro an example:
Let's say there are 100 families who have babies. 50 have boys an 50 have girls. Of the 50 who had girls, 25 have boys as 2nd child and 25 have girls. Of the 25 who have girls, 12 have boys and 12 have girls - and so and so forth. At every stage the number of boys and girls is the same and hence no change!

6:22 PM, June 29, 2006  
Blogger Karthik Nagaraj said...

Dinesh,
Welcome aboard. What happens if instead of 50 families getting boys and 50 getting girls, 75 get girls and 25 get boys. Then in the first round itself wouldn't the ratio be distorted? Its not 1:1 now! What happens then accoding to your reasoning?

11:02 AM, June 30, 2006  
Anonymous Dinesh said...

I used the 100 number for illustration (too lazy/dumb to figure out math represenation). Over the long term, given equal probability of boy and girl assumption, there will be 50 boys and 50 girls (or 50 lakh boys for 50 lakh girls). Even if there are 75 boys and 25 girls in one generation, this will balance out in the long run!

3:05 PM, June 30, 2006  
Blogger Karthik Nagaraj said...

Thought I could throw you off track there, but nahhhh, Good reasoning! Yes, it is correct whatever Dinesh says. Again fellas, this is a typical case of the law of chances. A mother can get a boy or a girl with 50 % chance (lets rule out all other unknown existing possibilities for now :)). So in the long run if we sample the number of boys to the number of girls, then we will have a balance among the boys and the girls. The key here is that this process continues forever. It is not a finite set - the girls grow up and again the same law of chances hold good for them and this process continues.

So the ruler's idea sucks bigtime and obviously he/she cannot get an abundance of girls in the land, for whatever reason the proposition was put in the first place. So this puzzle is SOLVED! Dinesh gets the credit. Good job there! So time for another one!

3:16 PM, June 30, 2006  

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