Suppose a couple will continue having children until they have at least two children of each sex (two boys and two girls). how many children might they expect to have?

after 4 children, there is 37.5% chance you have 2 boys/2 girls

 after 5 children, there is 62.5% chance you have at least 2boys/2 girls 

after 6 children, there is 78% chance you have at least 2boys/2 girls 

after 8 children, there is 93% chance you have at least 2boys/2 girls ... 

based on this i would say a reasonable expectation would be about 6 children

I hope this answer helped you somehow.

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