# Tag Info

### Should I choose Cox-based Jaynes' approach or Kolmogorov approach to base myself on to teach probabilities to high-school students?

I think you should (and likely will have to) use the assigned text and approach. It's incredibly unlikely you will just derive some new approach. That's not how high school teaching works. And on ...
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### Special topics for introductory probability

A classic application of Bayes' Theorem is in medical testing, and the difference/conversion between "what is the probability I test positive, given I have the condition" vs. "what is ...
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### Should I choose Cox-based Jaynes' approach or Kolmogorov approach to base myself on to teach probabilities to high-school students?

I would recommend avoiding foundational issues when teaching probability at a low level. At the high school level one mostly deals with finite probability spaces and the normal distribution. The ...
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### How to prove, without the LOTUS formula, to student that $V[aX+b]= a^2 V[X]$?

I think you will want to start by convincing the audience that $p(aX+b = ax_i + b)$ is equal to $p(X=x_i)$, probably with examples. I am not an expert statistician so please let me know politely if I ...
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### Should I choose Cox-based Jaynes' approach or Kolmogorov approach to base myself on to teach probabilities to high-school students?

I'm not familiar with Cox approach at all, so I cannot provide a qualified comparison, but I find the Kolmogorov's axioms pretty easy to comprehend and use and I'll try to explain why. No matter what ...
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### How to prove, without the LOTUS formula, to student that $V[aX+b]= a^2 V[X]$?

This is a consequence of the definition of the variance (1) the linearity of expectation (2) and an algebraic manipulation (3): V(aX+b)\stackrel{(1)}{=}\mathbb{E}(aX+b-\mathbb{E}(aX+b))^2\stackrel{(...
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### Correct notation of a Sample space

It's true that you typically refer to a random variable by a capital letter (e.g., $X$) and a particular value by a lowercase letter (e.g., $x$). So, $P(X = x)$ would represent the probability that ...
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### Special topics for introductory probability

One example of elementary probability is the so-called Birthday problem which asks for the probability that in a room of $n$ people two will share the same birthday. Sometimes formulated as a paradox ...
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### Special topics for introductory probability

You might already be aware of this one, given how famous it is, but the first thing that comes to my mind is the Monty Hall Problem. It doesn't require any fancy mathematical machinery, just a basic ...
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### Should I choose Cox-based Jaynes' approach or Kolmogorov approach to base myself on to teach probabilities to high-school students?

Should I choose Cox-based Jaynes' approach or Kolmogorov approach to base myself on to teach probabilities to high-school students? My answer is: No, you should not do that. These theoretical ...
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### Should I choose Cox-based Jaynes' approach or Kolmogorov approach to base myself on to teach probabilities to high-school students?

"I am planning to become a math high-school teacher" So it seems to me that you expect too much from high school students. I made the same mistake, the true is the vast majority of them will ...

### Special topics for introductory probability

Bertrand's Paradox is an old saw. The point is that trying to randomize an experiment is tricky since there can be different points of view.
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### Why can't I teach that picking (un)popular integers doesn't lower Probability of winning lotteries?

I'd say (time permitting) put it to a practical test. Take a standard 6-sided die, say you're going to roll it 100 times. You (the instructor) guess "1" every time, while the student can ...
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### Why can't I teach that picking (un)popular integers doesn't lower Probability of winning lotteries?

Did you consider the fact that your students have a point? When playing the lottery, let's say that the numbers $1$, $2$ and $3$ are popular, while $4$ is not. Being a popular number means that ...
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1 vote

### Special topics for introductory probability

[Additional to previous answer--can't edit, sorry.] dt688: I would be very wary about being too difficult or particular, when teaching in a corporate environment. I.e. if GMers are your target ...
1 vote

### Online Probability Simulation for Compound Events

It's really easy to write a script to do this, so I wrote one for you that runs entirely in the browser and allows you to edit the sample space elements: https://www.pythonmorsels.com/p/24dps/ Just go ...
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1 vote

### Seeking References on Deterministic and Stochastic Phenomena Suitable for High School Students

There was a question "is throwing dice a deterministic or stochastic process" on Physics.SE a while back, and I think this answer is insightful and accessible enough to spur a good ...
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1 vote

### How to explain that winning the lottery is not a 50/50 distribution?

Roll a die. Say, it will either roll a "1" or not, right? So the probability of rolling a "1" is 50%, yes? Say, it will either roll a "2" or not, right? So the ...

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