Question 866140
Here is a tree diagram depicting all the possible ways to have 4 kids


<img width = "500" src="http://i150.photobucket.com/albums/s91/jim_thompson5910/tree_zps53b06649.png">


The first column (of just 2 choices) represents child #1. 



If we stop at the second column, and ignore everything past it, then we see that there are 2^2 = 4 ways to have 2 kids (and those ways are shown in the tree diagram)



Likewise, if we stop at column #3, then we see all the possible ways to have 3 kids (2^3 = 8 different ways)



The last column is that last and 4th child. There are 2^4 = 16 ways to have 4 kids. Each possible path you trace (from the starting node to either a B or G in the fourth column) generates a sequence of 4 letters (either B or G) that represents a combination of boys and/or girls. For example, trace along the very top branches and you'll only pick up B, B, B, B or BBBB which represents all 4 kids being boys.



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Let's highlight all of the paths that have exactly 2 boys and exactly 2 girls.



Here is one path


<img width = "500" src="http://i150.photobucket.com/albums/s91/jim_thompson5910/bbgg_zps281a6be4.png">


This is the sequence BBGG which means the first two kids are boys, the second 2 are girls (boy, boy, girl, girl)


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Here is another


<img width = "500" src="http://i150.photobucket.com/albums/s91/jim_thompson5910/bgbg_zps1e2982bd.png">



That is the sequence BGBG (boy, girl, boy, girl)



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Here is another


<img width = "500" src="http://i150.photobucket.com/albums/s91/jim_thompson5910/bggb_zps368ee9bc.png">



This sequence is BGGB (boy, girl, girl, boy)



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and here is another path of exactly 2 girls, 2 boys


<img width = "500" src="http://i150.photobucket.com/albums/s91/jim_thompson5910/gbbg_zps7d735261.png">


This sequence is GBBG (girl, boy, boy, girl)



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and here is another path of exactly 2 girls, 2 boys


<img width = "500" src="http://i150.photobucket.com/albums/s91/jim_thompson5910/gbgb_zpsa66f5211.png">



This sequence is GBGB (girl, boy, girl, boy)



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and finally, here is the last path that represents exactly 2 girls, 2 boys


<img width = "500" src="http://i150.photobucket.com/albums/s91/jim_thompson5910/ggbb_zpsdad0dca2.png">


This sequence is GGBB (girl, girl, boy, boy)


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There are 6 sequences highlighted above and they are


BBGG
BGBG 
BGGB 
GBBG 
GBGB
GGBB


So there are <font color="red">6</font> ways to have 2 boys and 2 girls (they are shown above).



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To calculate the probability of having 2 boys and 2 girls, you divide that last number we found (6) by 16. This is because there are 16 ways to have 4 kids (2^4 = 16)



So, {{{6/16 = 3/8}}}



The answer as a fraction is {{{3/8}}}



Now use a calculator to get {{{3/8 = 0.375}}}



The answer as a decimal is <font color="red">0.375</font>



And multiply that decimal result by 100 to convert it over to a percentage 0.375*100 = 37.5%



The answer as a percentage is <font color="red">37.5%</font>