SOLUTION: if a couple plans to have 10 children whats the probability of them having at most 3 girls

Use a table.  

You probably have a cumulative binomial table in your
book.  If you can't find it go to this site:

http://www.pindling.org/Math/Statistics/Textbook/Functions/Binomial/cum_binomial_9_12.htm

That's an "at least" table, not an "at most" table, so we have to interpret
"at most 3 girls" as "at least 7 boys", which you must agree, is the
same thing.  So:  

locate n=10 and go across to p=0.5 and go down to 7 (at least 7 boys)
and read 0.171875.  That's the answer.

If your book has an "at most" table then you would red that value at 3.

Some books only have a binomial table that is not cumulative, like this
table:

http://www.pindling.org/Math/Statistics/Textbook/Functions/Binomial/binomial_9_12.htm

If yours is like that you have do your own accumulating by locating
n=10, going across to 0.5 and reading 

0.000977 fot exactly 0 girls
0.009766 for exactly 1 girl
0.043945 for exactly 2 girls
0.117188 for exactly 3 girls

and adding those probabilities together which will give you 0.171876.
The difference in that last decimal place is due to the fact that
the numbers in the table are rounded off.

The table in your book may not carry the decimals out that far.

Or you can do it on your TI-84 calculator:

On your TI-84 calculator:

Press ON
Press CLEAR
Press 2ND
Press VARS
Press ALPHA
Press APPS   (the letter B)

You should see -->  binomcdf(   followed by a blinking cursor

Type this after that --> 10,.5,3)

you should now see this --> binomcdf(10,.5,3)

Press ENTER

read  .171875

You can also do it by formula, but that's more tedious. But if
you must do it by formula, post again, and we'll show you how
to do that, too.

Edwin