# 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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### 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. ...
12k views

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

When casually discussing with my 13 yo child about probabilities, he told me there is a 50% chance to win at the lottery To what I said no, there is a 1 chance over 90 million (I roughly estimated ...
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 ...
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) ...
1k views

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 ...
905 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, ...
552 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 ...
1k views

### 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 ...
727 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 ...
2k 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 ...
299 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 ...
880 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 ...
232 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 ...
169 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. ...
95 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 ...
456 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. ...
170 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 ...
111 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 ...
299 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 ...
82 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 ...
125 views

### Difficulty in explaining sample space

I am running into problems explaining to my students in high school what exactly is sample space in probabilities, especially with identical objects. For example, according to Q6.2.3 of this UIC ...
261 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 ...
180 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 ...
120 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 $X$ ...
92 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 ...
150 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 ...
285 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 ...
98 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 ...
292 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 ...
171 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) \...
275 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 ...
84 views

### EdX Courses for Self-Study

I have been independently considering two edX courses in mathematics. The first, a course on probability theory drawing from a financial crisis case study, appeared to me plausibly comparable in ...
135 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 ...
88 views

256 views

### Best resources for probability/statistics textbooks

I'm looking for a good textbook introduction to probability/statistics that a first/second year undergrad math student could use! I'd like a book that emphasizes theory over procedure. I'd prefer an ...
142 views

### What story and one-digit Natural Numbers best fit Bayes' Theorem chart?

Some students have sniveled that most examples of Bayes' Theorem use non-integer numbers. I want to try a Bayes' Theorem chart that uses just single digit Natural Numbers $\le 9$. To complete the ...
150 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 ...
164 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 ...
150 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 ...
97 views

### How to emulate erf and/or the Normal Inverse function in Moodle?

I've just discovered "calculated questions" in Moodle and I'm trying to create a simple one where I would be asking the student to find the probability that an observation from a standard normal ...
118 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 ...
118 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 ...
196 views

### Cautionary tales for Gaussians/the central limit theorem?

In any undergraduate course on probability, one of the fundamental results that is discussed is the central limit theorem. Apart from the interesting mathematics needed to prove the result (most often ...
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 ...