# Tag Info

Accepted

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

Your child is using the Principle of Insufficient Reason, which states that if we have no information about something other than the set of possible outcomes, then we should assume that all outcomes ...
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### How to explain that winning the lottery is not a 50/50 distribution?

I don't think that talking about probabilities formally would be to any benefit for your son. However, you could simulate a lottery at home, using a die. Say that a player wins if they guess right the ...
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### How to explain that winning the lottery is not a 50/50 distribution?

I think so far best reaction is the top-voted comment: Have you asked him to explain what he thinks “probability” means? I'd address the topic from here. And as this is not a school environment when ...
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### How to explain that winning the lottery is not a 50/50 distribution?

Without going into the mathematics too deeply, I would say it boils down to this: There is only one way of winning the lottery: guessing all the numbers correctly. But there are a lot more possible ...

### 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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### Why do you need to distinguish between apparently identical objects in probability?

The answers provided here so far give lots of good tips but I think they're not addressing a key part of the question, which is "why do we need to count two events (50,52) and (52,50), instead of one ...
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### How to explain that winning the lottery is not a 50/50 distribution?

A slightly different approach: Let's say there are 100 lottery tickets in total and there is only one ticket that will win you the prize. If you don't buy any tickets at all, what's your chance of ...
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### How to explain that winning the lottery is not a 50/50 distribution?

Make it Personal Take a marshmallow (or some small candy that you know he likes), show it to him, then put it into one hand behind your back and say: "If you pick the hand with the marshmallow, ...

### Common misconceptions in high school probability curriculum

Here are some things I occasionally encounter in the first few tutorial sessions as a TA for an undergraduate introduction to probability theory/statistics course. Why "and" corresponds to ...

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

Taking the ed part of the question: Don't feel like you have to convince the kid of everything immediately. Give him time. In particular, watch out for him just trolling you. If you do decide to ...
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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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### Monty Hall challenge

If you "stay" then you win when the prize is behind the one door your originally selected, yet when you "switch" you win when the prize is behind one of the two doors you originally did not select.
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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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### 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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### Real-world Markov chains

I'm not sure if you consider the board game Monopoly as a real-world example, but it is often used to explain Markov Chains to laypeople. Ian Stewart has a couple of Mathematical Recreations articles ...
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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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### Moving from discrete probability distributions to continuous ones

This is an uncomfortable moment, mathematically, in a non-calculus-based statistics course; frankly, we simply need to steal the calculus concept and hope that students trust us about it, without ...
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### Why do you need to distinguish between apparently identical objects in probability?

This is a very good question. The issue comes up frequently. I explain this using a toy model: throw two regular six-sided die. What is the probability that the sum is 3? With some physical modeling, ...
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### How to explain that winning the lottery is not a 50/50 distribution?

Ask him whether the probability of winning is the same if you bought 1000 tickets rather than one ticket. Or, imagine a lottery with 100 tickets, of which only one was a winner. If 100 different ...
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### How to explain that winning the lottery is not a 50/50 distribution?

I want to offer a game to play with your son that he would almost definitely understand and would impart the principles of probability (and the futility of gambling at the same time). First, get some ...
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### What story and one-digit Natural Numbers best fit Bayes' Theorem chart?

Two professional athletes and six fans are eating at a restaurant table. Both of the professional athletes are wearing their jerseys, while only half of the fans are wearing jerseys. Given a person ...
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