> The applet for three pancakes does not work.

I just checked. It does in my browser.

> You give two solutions for that probability; one is 1/2 and
>the
> other is 2/3.

No, there second is 1-2/3. The wording is perhaps begging.

> To me the question asked is equivalent to question: What is
>the probability that you got a pancake Brown on both sides,
>and that is
> clearly 1/3. Am I wrong?

No, you are right, but "clearly" may be questioned by many budding mathematicians.