{"id":375,"date":"2010-03-12T17:14:45","date_gmt":"2010-03-12T21:14:45","guid":{"rendered":"http:\/\/mattfife.net\/wordpress\/?p=375"},"modified":"2010-03-12T17:14:45","modified_gmt":"2010-03-12T21:14:45","slug":"question","status":"publish","type":"post","link":"https:\/\/mattfife.com\/?p=375","title":{"rendered":"Google interview question"},"content":{"rendered":"

In a certain country, a family continues to have children until they get a boy.\u00a0 When they get a boy, they have to stop having children. \u00a0 Otherwise, they keep going.\u00a0 Assuming there is always a 50\/50 chance of a boy\/girl when having any one kid and nobody stops ‘early’ – what’s the ratio of males to females in such a society?<\/p>\n

Answer(spoilers):<\/strong>
\nAt first your gut tells you there needs to be more females than males – after all, there’s going to be families out there with 2,3,4,5 or even more girls.\u00a0 Yet only 1 boy.\u00a0 However, if you start thinking about it this way, a shocking revelation comes:<\/p>\n

A families first birth:
\n1\/2 = boys -> they stop here, no girls at ALL in 1\/2 the households
\n1\/2 = girls -> they go on….<\/p>\n

2nd birth for those families with one girl:
\n1\/2 = boys -> they stop with 1 girl, and 1 boy
\n1\/2 = girls -> they go on….<\/p>\n

so now it becomes a sum of:
\nboys = 1\/2 + (1\/2)*(1\/2)+ (1\/2)*(1\/2)*(1\/2) + (1\/2)*(1\/2)*(1\/2)….
\ngirls = 1\/2 + (1\/2)*(1\/2) + (1\/2)*(1\/2)*(1\/2) + (1\/2)*(1\/2)*(1\/2)…<\/p>\n

Whaaaa?? – its the SAME.\u00a0 Yep – the count of the number of boys and girls will be the same.\u00a0 See, we forget that 1\/2 of the families will have NO girls at all – and that’s a big smack to the overall number of girls.\u00a0 Sure, there may be families with 2,3,4 or more girls, but always one boy – and that combined with the fact half the population’s families will only have a single boys child equals out.\u00a0 Crazy but true.<\/p>\n","protected":false},"excerpt":{"rendered":"

In a certain country, a family continues to have children until they get a boy.\u00a0 When they get a boy, they have to stop having children. \u00a0 Otherwise, they keep going.\u00a0 Assuming there is always a 50\/50 chance of a boy\/girl when having any one kid and nobody stops ‘early’ – what’s the ratio of males to females in such a society? Answer(spoilers): At first your gut tells you there needs to be more females than males – after all,…<\/p>\n

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