66 votes
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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55 votes

How to explain Monty Hall problem when they just don't get it

For some reason, the 'extend it to 100 doors and eliminate 98' explanation doesn't make it any clearer for me. Rather than talk about probabilities as fractions, I explain it this way: "If you ...
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46 votes

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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29 votes
Accepted

How to explain Monty Hall problem when they just don't get it

Your explanation, by the way, is very elegant. As an experienced mathematician, I see immediately that it cuts right to the heart of the matter and admits no ambiguity. Unfortunately, this is ...
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  • 1,083
27 votes

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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25 votes

Probability Misconception: Two Bags with Black and White Marbles

Firstly, don't forget that your student has thought hard to come up with his answer and to be told it is wrong may be taken as invalidating his effort, or even insulting his intelligence. This might ...
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20 votes

How to explain Monty Hall problem when they just don't get it

There isn't any sure-fire method of explaining anything, and especially in math. But specifically in the case of the Monty Hall problem it has been proven by extensive experience that many individuals ...
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19 votes

How to explain Monty Hall problem when they just don't get it

Perhaps it's not the explanation that's the problem. I suggest you have them explain to you their understanding of the problem. Listening to their justification might reveal why your explanation is ...
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  • 7,385
16 votes

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 ...
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14 votes

How to explain Monty Hall problem when they just don't get it

I've had best luck by simplifying the problem to asking whether you want to pick one door or two doors. Everyone understands they'd be better off picking two doors. At that point I tell them to just ...
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14 votes
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What is a good way to explain the Lebesgue integral to non-math majors?

As you told the student, the easiest way is to regard the Lebesgue integral as beginning with a partition of the range, rather than the domain. Perhaps a more refined way to view this is that the ...
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14 votes
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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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13 votes

How to explain Monty Hall problem when they just don't get it

I found the most helpful way to think about the problem is to expand it to a larger number of doors. For example, if you have them select from 100 doors, where 99 are losers and 1 is a winner. Then ...
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12 votes

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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10 votes

Why we mistaken coin toss to be an example of classical probability?

One often sees the phrase "a fair coin." So, if you wish, this is a theoretical object which does not exist in the real world but the name is evocative and useful. In real life a (real) coin flip is ...
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9 votes

Explaining the "siblings" paradox

I think there are a few independent questions here that can be considered teaching mathematics (I will not broach the subject of how to solve the problem). First, there is: How can you state this ...
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9 votes

How to explain Monty Hall problem when they just don't get it

I never understood it until my Maths lecturer explained it to me. Unfortunately I can't remember the exact way he explained it, but I'll try my best to remember. I really like your own explanation, so ...
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9 votes

How to explain Monty Hall problem when they just don't get it

The best sure-fire method for teaching this to people who don't want to learn it is to set up a Monty Hall style game for small stakes of real money. When they start losing 2/3 of the time, they will ...
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9 votes

Probability Misconception: Two Bags with Black and White Marbles

Ask whether they think putting the marbles in a bag into any particular arrangement would affect the outcome. If they're ok with this, have them consider the arrangement of Bag 2 where the marbles are ...
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9 votes
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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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9 votes

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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  • 284
9 votes

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, ...
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8 votes

Probability Misconception: Two Bags with Black and White Marbles

DavidButlerUofA's answer hits the spot on pedagogical methodology. However, the actual question is about establishing the correct intuition. With that said, a good way to falsify the wrong intuition ...
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8 votes

What is a good way to explain the Lebesgue integral to non-math majors?

To see the reason why Lebesgue integral is preferred in probability theory one must go beyond the setting of real functions $f \colon \mathbb{R} \mapsto \mathbb{R}$. In this setting both the Riemann ...
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8 votes

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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7 votes

How to explain Monty Hall problem when they just don't get it

While your explanation is correct, and easily understood by people like us, it's a bit too terse (a quality we like) for a lay person to understand. You can simply expand on it. And most importantly ...
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7 votes

What is a logical way to introduce probability and statistics to students that don't know fractions or percentages yet?

I'm going to suggest what you're considering is very difficult. And also, I don't think it's something I'd want to do. (But we'll do it below anyway, for fun!) Fractions are an early concept that ...
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7 votes

Probability Misconception: Two Bags with Black and White Marbles

One suggestion that might be worth considering is asking the students the same question but for a bag with no white balls. Suppose you have a bag with 1 black and no white balls ( probability of ...
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7 votes

Probability Misconception: Two Bags with Black and White Marbles

I wrote a long answer to this, which then made me realise that I think this needs the rule. [Restart:] A few pointers first: Don't number the bags if you have numbers of marbles: big/small, black/...
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