Background: I’m not exactly a Math educator, but I’m currently a TA of an elementary algebra course aiming at students of age 14-15.

I found that a lot of people have misconception about probability theory. Usually, when the (undergraduate) course director from my department encourages us to take the introductory probability course (a 3000-Level one), not so many students follow his advice. While he emphasized that learning probability theory is useful (for example, as a preparation for advanced courses like Financial Maths and Stochatic Processes), students don’t take the advice seriously. Instead,

  1. students who struggle in both analysis and algebra find it hard to fulfil the graduation requirement, and take the probability course because they think it is easier;

  2. students who are good at analysis or algebra think that probability theory is too applied (and in fact it isn’t...the course starts at the Kolmogorov axioms and ends at an elementary proof of the Strong Law of Large Number, and exams are all about proofs);

  3. students who love applied stuff (in particular Statistics) have usually chosen Statistics as their major, and they take their STAT courses instead of MATH courses.

This misconception doesn’t only appear in the department. During the tutorial I talked to some (young) students. Unfortunately, their understandings on probability theory only concern elementary combinatorics (such as finding out the number of ways to take out r objects out of n objects with certain constraints, which, I admit, is not quite Math-like compared to other subjects such as solving equations).

I did take the probability course as a major elective one and I find it interesting. However, I’m not sure whether I should rectify others’ misconceptions concerning probability theory, and if I should, how I should do so (perhaps as a piece of advice given to students/close friends at year 1-2).

Any help is appreciated.

Edit: Essentially I’m asking: A lot of students think that probability theory is too applied, and this is certainly a misconception. How to clarify what probability theory actually involves (as an incentive for them to take the course), perhaps only using a few words? (e.g. during a short discussion concerning course selection) This aims at persuading students who come from either pure (who think that probability theory is less theoretical) or applied (who treat the probability course as a very easy one) background.

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    $\begingroup$ I think the fact that there is so much excitement about AI / machine learning / data science right now helps provide some motivation, because probability is important for those subjects. Also, I think the perspective that probability is an extension of logic that allows us to reason about uncertain beliefs makes probability sound pretty cool. (This viewpoint is championed in Jaynes's book Probability: The Logic of Science, for example.) Probability has some wonderfully unintuitive results that make the subject fun, and the central limit theorem is beautiful (where do $e$ and $\pi$ come from?) $\endgroup$ Commented Jul 20, 2018 at 2:11
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    $\begingroup$ At the moment, I am not quite sure that I understand exactly what your question is. It seems to me that you are asking about how you should advise your students (which further seems like you are seeking personal advice, which doesn't really fit with the ethos of SE). Could you please edit your question to make it more clear what you are asking? $\endgroup$
    – Xander Henderson
    Commented Jul 20, 2018 at 3:45

1 Answer 1


Perhaps you could give a sample of the important central subjects of study. I would say something like:

In this course, we will utilize basic axioms to prove many results, culminating in the Law of Large Numbers: in the limit that the number trials goes to infinity, the observed average converges to its theoretically expected value. Calculus and proof-reasoning are heavily utilized.

It signals the following:

  • this is a 'real' math course with proofs, not just combinations/permutations.
  • the depth of the course; interested students know that the course culminates in the Law of Large Numbers, so they have a better idea of how applied it is.

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