bonanova Posted June 27, 2009 Report Share Posted June 27, 2009 A nice counterintuitive puzzle asked the ratio of boys to girls in a village where the rule was to stop having children after the first son was born. If you haven't solved it yet, you might want to give it a try. Here's a follow-on. If all the families obeyed this rule, and continued having children until a son was born, then stopped, what is the average size of a family? Quote Link to comment Share on other sites More sharing options...
0 Guest Posted June 27, 2009 Report Share Posted June 27, 2009 P(g) = P(b) = 1/2 Now considering that in all the families the arents are also alive, then Probability of 1 child (first born is a boy) = P(b) = 1/2 = probabiity that the family size is 3 Probability of 2 children = P(g)*P(b) = 1/4 = probability that the family size is 4 Probability of 3 children = 1/8 = probability that the family size is 5 and so on So, the avg expected family size in the village is: 3(1/2) + 4(1/4) + 5(1/8) + ... = 4 Quote Link to comment Share on other sites More sharing options...
0 Guest Posted June 27, 2009 Report Share Posted June 27, 2009 4 Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted July 4, 2009 Author Report Share Posted July 4, 2009 Both correct. Quote Link to comment Share on other sites More sharing options...
Question
bonanova
A nice counterintuitive puzzle asked the ratio of boys to girls in a village
where the rule was to stop having children after the first son was born.
If you haven't solved it yet, you might want to give it a try.
Here's a follow-on.
If all the families obeyed this rule, and continued having children until
a son was born, then stopped, what is the average size of a family?
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Share on other sites
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