Adding Binary Numbers confusion

Addition of two Binary numbers.

Video Shows:

 0010
 1111
-------
 0010


But based on what I'm reading about how to add binary, adding two "1"'s gives you a "10" (you put a "0" and carry the 1)
Using the methods I'm finding online for adding binary numbers, I get this:

 11    <-carries

 0010
 1111
-------
10001


I also added the numbers in this online calculator:
http://www.calculator.net/binary-calculator.html?number1=0010&c2op=%2B&number2=1111&calctype=op&x=44&y=10


The above page also outlines the method of adding binary numbers:

Binary Addition -The addition of binaries is similar to the decimal system. The only different is to carry over when the result is 2.

0 + 0 = 0
0 + 1 = 1
1 + 0 = 1
1 + 1 = 0, carry 1 = 10