67
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 ...
- 823
49
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 ...
- 1,120
28
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 ...
- 437
17
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 ...
- 171
15
votes
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 ...
14
votes
Accepted
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 ...
- 256
13
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 ...
- 231
12
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, ...
- 651
10
votes
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 ...
- 201
10
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 ...
- 304
10
votes
Accepted
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 ...
9
votes
Accepted
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.
- 7,722
9
votes
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 ...
- 3,939
9
votes
Accepted
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 ...
- 5,869
9
votes
Accepted
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 ...
- 21.7k
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 ...
- 10.9k
8
votes
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{(...
- 1,411
7
votes
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 ...
- 26.4k
7
votes
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, ...
- 11k
7
votes
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 ...
- 655
7
votes
Difficulty in explaining sample space
The (correct) sample space depends on how the probability problem has been framed:
The set of letters in “$MISSISSIPPI$” is indeed $S_1=\{M,I,S,P\}.$
In a probability experiment with sample space $...
- 1,832
7
votes
Probability — analytical results instead of simulations
Your question could apply generally to why should anyone learn the math "behind" anything, if they can easily compute the answer on a computer. I don't think they ALWAYS should. There should ...
- 343
6
votes
What is a good way to explain the Lebesgue integral to non-math majors?
I have the impression that the underlying problem is the expected value itself, not the integral (on which the expected value is based, of course). But since the question asks about the integral, I ...
6
votes
Moving from discrete probability distributions to continuous ones
This is treason, but anyway:
If your students can jump from "ratio of outcomes in $A$ over all possible outcomes" to "ratio of length of interval, over total feasible length", then the answer why ...
- 1,552
6
votes
Accepted
Real-world Markov chains
The Markov Chains I work with are usually called in the epidemiological and in the chemistry literature "compartmental models". The most famous (from an epidemiological viewpoint) is the SIR model for ...
- 336
6
votes
Accepted
How to explain the sample space of Monty Hall problem?
I think the key here is that $(C, G_1)$ and $(C, G_2)$ are each only half as likely as each of the other two cases - and the standard "counting" approach to probability only works if all the cases are ...
- 1,994
6
votes
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 ...
- 271
6
votes
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 ...
- 5,629
6
votes
Not sure what a student is misunderstanding on this Stat question
I see a few things going on here that may be confusing your student.
The problem itself is a problematic one; it assumes but does not state that seniority is independent of position, and that the ...
- 1,994
6
votes
Common mistakes in probability
These two concepts from elementary probability are not that elementary to digest.
If, in a probability experiment, event B's outcomes are restricted due to knowing that event A happens, the two ...
- 1,832
Only top scored, non community-wiki answers of a minimum length are eligible