Questions tagged [probability]

For questions about the teaching of probability, dealing with students misconceptions in probability, and explaining probability theory paradoxes.

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Teaching probability with motivating examples [closed]

Are there any books that illustrate concepts and theorems in probability which address: Why do the various theories hold, and how we can understand them, rather than just stating and proving theorems?
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9answers
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Why do you need to distinguish between apparently identical objects in probability?

In the math class I taught today I was asked a question, and I was unable to give a good answer. The problem was as follows: A certain factory produces throat tablets. In each pack, there are from 48 ...
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1answer
198 views

The most transparent exposition of Bayes' Theorem

I am seeking the most transparent exposition of Bayes' Theorem (for undergraduates). I would prefer to avoid mentioning "prior" and "posterior," and instead focus on frequencies. The Wikipedia entry ...
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2answers
78 views

A Markov chain demonstration that doesn't require computers

I have a large probability class and would like to do some memorable demonstrations of Markov chains for them. Does anyone have any recommendations for a "low-tech" demo that doesn't involve ...
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2answers
125 views

Better ways to explain mutually exclusiveness and dependency of events

I am teaching probability on mutually exclusiveness and dependency of events. Let me take a simple example as follows. A box contains 2 red balls and 3 purple balls. They are identical except for ...
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1answer
126 views

What does “Four selected students are not born in the same months” mean?

I am teaching on probability. I found a question that seems to be ambiguous as follows. Four students are randomly chosen from a place. Assuming the birthdays of people are equally likely to occur ...
4
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1answer
107 views

How to explain the sample space of Monty Hall problem?

I am now pretending to be a newbie student. I write the following sample space for the Monty Hall problem (It is a famous brain teaser, I assume you know it). $$ S=\{ (C,G1),(C,G2), (G1,G2), (G2,G1) \...
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1answer
109 views

Why emphasize moment generating function over characteristic function in a probability course?

I've noticed that some undergraduate introductory probability textbooks and courses emphasize or seem to prefer the moment generating function $m(t) = \mathbf E(e^{tX})$ of a random variable $X$ ...
4
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1answer
131 views

Encouraging students to learn probability

Background: I’m not exactly a Math educator, but I’m currently a TA of an elementary algebra course aiming at students of age 14-15. I found that a lot of people have misconception about probability ...
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0answers
87 views

What is the best term for “probability measure” in an undergrad introduction to probability course?

The function $P$ that takes an event $A$ as input and returns the probability $P(A)$ as output is called a "probability measure" when we are developing probability using measure theory. I have also ...
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2answers
93 views

Urn (containing colored balls) generator?

I am looking for a nice app that would enable me to create "automatically" nice urns filled with balls of two different colors, following the illustration below (actual colors do not matter, being ...
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1answer
136 views

Why aren't Bayesian Networks and Variable Elimination introduced earlier?

Throughout my undergrad, I dreaded probability. I hated it, I was horrible in it, I just never got it, and felt stupid when the professors used "summation/marginalization" equations out of the blue to ...
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6answers
214 views

Neat topics or problems to include in a probability class

I'd like to get suggestions for neat topics or problems to include in an undergraduate, upper division Introduction to Probability class. Many people have taught probability for many years and I'm ...
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3answers
259 views

How to convince the following probability problem to highschool student?

I will present two problems alongside solutions, student is doing problems of type I like a cakewalk but has several issues with the problems of type 2; Type I Consider an experiment of rolling ...
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4answers
974 views

Real-world Markov chains

I will give a talk to undergrad students about Markov chains. I would like to present several concrete real-world examples. However, I am not good with coming up with them beyond drunk man taking ...
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0answers
144 views

Does this problem enhance mathematical creativity?

There are an equal number of red, yellow, green, and blue cards. Take one of them and put it in the box. Suppose that red cards was most selected, followed by yellow, green, and blue when we selected ...
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2answers
85 views

Examples showing necessity and advantage of emperical definition of probability

As the title, I want to ask for some examples showing necessity and advantage of emperical definition of probability in teaching high school students. We knew that the classical definition has some ...
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3answers
86 views

How to best explain that the sum of conditional probabilities still sum to 1

I am comfortable with explaining to my high school students that for an event $A$ we have that $P(A) + P(A^C) = 1$ But what is the best way to help students realize that $P(A \mid B) + P(A^C \mid ...
16
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4answers
635 views

Common misconceptions in high school probability curriculum

I am teaching probability to high school students. The material we are covering is pretty standard and includes: Introducing how to calculate the probability of events, e.g. coin flips, card draws, ...
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5answers
537 views

Moving from discrete probability distributions to continuous ones

I'm teaching an introductory statistics class at a community college, and we've just finished a unit on discrete probability. At the moment, the students' conception of the probability of an event A ...
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3answers
156 views

Mathematical Task with Various Solutions

I need to come up with a mathematical task for middle school (9th grade), which involves either algebra, functions, probability or statistics (anything but geometry actually). My problem is, that the ...
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0answers
72 views

Literature on teaching and learning probability

In an earlier question, the book Exploring Probability in School (2005) (Link) was mentioned. It gives an overview of the research on the teaching and learning of probability up to that point. Does ...
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3answers
247 views

Monty Hall challenge

Thinking about the counterintuitive Monty Hall Problem (stick or switch?), revisited in this ME question, I thought I would issue a challenge: Give in one (perhaps long) sentence a convincing ...
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3answers
83 views

Example illustrating use of additivity of (probability) measures before introducing independence and conditioning

I would like to be able to illustrate why additivity is a natural property to assume for probability measures. While it is relatively simple to give a short hand waving intuitive analogy to volume or ...
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2answers
130 views

suggestion for probability and stats text to suit my learning style.

I am of a mature aged learner and want to learn probability and statistics at a senior high school (k12) and undergraduate level for my own general understanding. I have discovered in the past that I ...
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0answers
116 views

Is the absence of complex analysis a significant disadvantage in math grad school application? [closed]

I am a junior math major considering math grad school, possibly in probability theory. Would the admission commitee of math grad schools view the absence of complex analysis as a significant ...
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0answers
117 views

Basic Bayes rule problem [closed]

I was reading this article, and I decided to use the “canonical example” of a “precocious newborn observing his first sunset” as a problem for my students (undergrads in an intro to inductive logic ...
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5answers
215 views

Lesson-planning: Teaching probability concepts via geometry

I am intending to teach a lesson covering some topic related to "Probability via Geometry" and, if possible, I would appreciate references or materials (or good ideas) that can help me. The target ...
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4answers
158 views

Recommendations for free, basic resource on discrete probability for a discrete structures class?

I'm teaching a course this fall on Discrete Structures for Computer Science. It's taught out of the math department but is a service course for the CS department with 90-95% of students being CS ...
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1answer
107 views

How to teach steady state in queueing (if at all?)

I am teaching an undergraduate course in Operations Research to business students (they are not: maths students). I want to check, if and how teaching the steady state makes any sense. As in the ...
4
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1answer
83 views

A different version of central limit theorem?

When I was taking the probability class myself, I remember my professor give us a standard counter example of central limit theorem: Let $X_{i}\sim X$ be $i.i.d$ random variables. Let $E(X)=0, Var(X)=...
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1answer
153 views

Is there any footage of Let's Make a Deal illustrating the Monty Hall problem?

The Monty Hall problem is a classic probability riddle and I will be gleefully explaining it to my class of discrete math students. It is apparently based on his classic game show Let's Make a Deal. ...
8
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1answer
374 views

“Probable” vs. “Likely”; Choosing the Appropriate Word

In some school textbooks, before introducing the probability as a number between $0$ and $1$, the words "likely", "More likely", "less likely" etc. are used to indicate the likelihood of an event. ...
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2answers
2k views

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

A few days ago I had my last discussion session on probability theory as a TA. In the end I asked students to ask me questions as this is the last class. One of the student asked me about the (real) ...
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14answers
4k views

Probability Misconception: Two Bags with Black and White Marbles

I asked this question in a class of 13-year-old students: Bag 1 contains 2 black marbles and 1 white one. Bag 2 contains 20 black marbles and 10 white ones. Which bag is more likely to yield a black ...
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4answers
569 views

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

It is now well known that a random coin toss has 1/6000 probability of landing on its edge. So the out-dated model that a coin toss always land on either heads or tails with probability 1/2 is wrong. ...
9
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0answers
80 views

How can instructors bridge the gap between an engineering course in stochastic systems and a more rigorous Stochastic Processes course?

Systems and electrical engineering graduate students often take a course on stochastic systems (a.k.a. "Probabilistic Systems Analysis"). A typical course will present such topics as multivariable ...
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6answers
815 views

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

Students are exposed to sets very early in their education, so my first inclination is that this would be the best method to give children in the early primary grades an introduction to probability ...
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4answers
951 views

Explaining the “siblings” paradox

This is a question I originally posted on Math Stackexchange. I've just seen a very good discussion of Monty Hall problem, and someone mentioned the "siblings" paradox. I've had some success ...
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22answers
16k views

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

Talking to some friends, I was asked to explain the answer to the Monty Hall problem (see also here;) .... they were having some trouble because whoever explained it to them didn't do a very good job. ...
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2answers
251 views

Where to get cuboid dice?

Anybody know where I could get some cuboid (but not cube) dice for use with teaching probability? Or advice on how to make some without a 3d printer? Edit: In response to comments seeking ...
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2answers
523 views

First year undergraduate text that teaches calculus using probability as a primary motivating example?

There has long been debate about whether a first year undergraduate course in discrete mathematics would be better for students than the traditional calculus sequence. The purpose of this question is ...
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1answer
272 views

Probability textbooks repository

(This question was posted more than two years ago on math.stackexchange.com and, although there were some worthwhile answers, none actually answered the question as phrased.) Has anyone compiled a ...