[llasram]

That we're modeling the outcome of a coin toss as a sample space set containing at least two event elements, one of which we call "heads," and that we have a probability measure which assigns 0.5 to the subset consisting of only the "heads" event.

[danbruc]

You are presupposing an understanding of probability, aren't you? What does it mean that a probability measure assigns 0.5 to heads?