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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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, ...
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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 ...
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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 ...
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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.
quid♦
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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
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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7
votes
Lesson-planning: Teaching probability concepts via geometry
I see at least one good topic for this: Monte-Carlo algorithm to compute area or volume. It has a strong geometric side, is definitely probabilistic, only involves simple concepts, and is even ...
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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, ...
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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 ...
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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 $...
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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 ...
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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
Lesson-planning: Teaching probability concepts via geometry
Here are some examples, many of them gleaned from this link. Note that this link has slides of an entire unit and would probably be very useful.
Find the probability of landing on different colors in ...
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6
votes
What is a logical way to introduce probability and statistics to students that don't know fractions or percentages yet?
When I taught second grade, we introduced probability without fractions. We would talk about different events and classify them as:
impossible
unlikely
equally likely and unlikely
likely
certain
...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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6
votes
Law of large numbers as a middle school topic?
You have two different questions.
Should?
I don't think your daughter has a choice here. So it's irrelevant to her. Obviously society has a choice. I don't think the topic is so awful, personally....
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