SOLUTION: The random variable x is the number of girls of 4 children to a couple that is equally likely to have a boy or a girl. Among all families with 4 children what is the average numb

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Question 1186830: The random variable x is the number of girls of 4 children to a couple that is
equally likely to have a boy or a girl. Among all families with 4 children what is
the average number of boys?
Found 2 solutions by ikleyn, Edwin McCravy:
Answer by ikleyn(52817) About Me  (Show Source):
You can put this solution on YOUR website!
.

The common sense says that this number is 2 (due to the symmetry boys - girls).



Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
It's pretty obvious that on the average they would have 2 boys and 2 girls.
There are 24 = 16 possible birth orders for the 4 children listed
below:

birth| number
order|  of
     | boys 
-------------
BBBB |  4
BBBG |  3
BBGB |  3
BBGG |  2
BGBB |  3
BGBG |  2
BGGB |  2
BGGG |  1
GBBB |  3
GBBG |  2
GBGB |  2
GBGG |  1
GGBB |  2
GGBG |  1
GGGB |  1
GGGG |  0
---------
 sum = 32
average = 32/16 = 2 boys.

Edwin