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## Family Problem

Probability puzzles require you to weigh all the possibilities and pick the most likely outcome.

 Puzzle ID: #45525 Fun: (2.4) Difficulty: (2.26) Category: Probability Submitted By: dalfamnest

The relatively unknown Mbwatzeze Tribe had a rather strange law restricting the size of families. Each married couple was expected to continue having children until they had EITHER one child of each sex OR a total of four children.

What was the average (mean) number of children born to each couple? (Assume that they kept to the law and that each couple had the maximum permitted by the law.)

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 dalfamnest Oct 23, 2009 Hi everyone! Hope you enjoy this little teaser. I thought it was a fun idea. How about some comments, please - it's my first Probability Teaser and I'd value some DEEF, + or -. [See today's TOTD!] valencia Oct 23, 2009 really good teaser had to think about that one!! good job on being the first one precious1026 Nov 15, 2009 It seems to me the answer is difficult to achieve without certain information. Perhaps, it's the formation of the Question, which appears to assert there is more families than the one given in the problem. Well, I guess the means of 2.75 is a logical number of children in a family. I would say, and I usually say "keep them coming, but I would be lying if I did say "keep them coming. What is the probability of you making up more problems such as this? Actually, this is a good teaser for those who understand the mean... javaguru Dec 30, 2009 Simple and fairly easy. You can simplify it further by ignoring male/female permutations as: .5 probability second child is different than first (2 kids); .5 x .5 = .25 that second child is same as first and third child is different than first (3 kids); .5 x .5 = .25 that second and third children are same as first (4 kids). .5 x 2 + .25 x 3 + .25 x 4 = 2.75 niket Oct 10, 2016 why the order id important in case of families with 2 children (M-F,F-M) are different, while this is not the case for families having 3 or more children