Are simple command variable assignments accessible in nested scripts? e.g., does `child.sh` have "FOO=BAR" when running "FOO=BAR ./parent.sh"?

Although this is easy to try and see, I was looking for the answer on StackOverflow and couldn't find it. That's why I'm asking and answering my question. I recommend reading this first. The answer is hinted at, but not directly stated. --- I have these two shell scripts:

$ cat parent.sh
echo $(basename "$0")
echo "$FOO"
./child.sh

$ cat child.sh
echo $(basename "$0")
echo "$FOO"

What will be printed if I run this command: FOO=BAR ./parent.sh