An answer that I was trying to answer on Quora, but was prevented from doing so by a technical fault: Why is probability a tough Subject, even for students who are very good at math?
Because probability as it manifests itself in real life is surprisingly deep and difficult concept. As a knowledgeable colleague once explained to me,
“There are at least four distinct interpretations of probability:
- objective Bayesianism
- subjective Bayesianism,
- a propensity theory
- a frequency theory
along with various pluralists positions.
Unless you work in artificial situations with, say, perfect dice, these differences, which I imagine most school teachers are unaware of, will confuse one’s teaching.
Odds in horse races provide a very good illustration of probabilities. Are they
- The unique propensity of a horse in that precise situation to win.
- The limiting frequency in some long series of events.
- A measure of subjective expectation, reflected in betting behaviour.
- An objective measure of the expectations of a rational agent given certain information.
The question is: what should we tell to children? At what age they become able to distinguish between “subjective” and “objective”?”