# 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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### Is it weird for an undergrad or grad quant/applied maths(/even pure maths) programme to not teach that probabilities of 0 or 1 will never change? [closed]

Edit: i didn't mean it like this programme should do this or that. i mean other people are accusing me like 'your programme should've had this or that' (actually they're saying that i should know this ...
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1 vote
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### Best books for mathematical statistics self-study?

I'm hoping to start a masters in mathematics in the fall, and am hoping to find a good book on mathematical statistics to study so that I'll be able to take graduate level mathematical statistics once ...
76 views

### Code for Urn (containing colored balls) generator? [duplicate]

I am interested in code that generates an urn with various colored balls for an economics experiment. I came across this thread: Urn (containing colored balls) generator? However, the server that the ...
257 views

### Probability — analytical results instead of simulations

After students learn how to use probabilistic simulations, what strategies can one use to encourage them to understand analytical results anyway? For example, I'm struggling to find a compelling ...
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1 vote
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### How can I effectively learn and master Math and Statistics for Data Science?

I completed a BSc in Computer Science recently and am going on to do an MSc in Data Science. However, the only focussed math module I had during CS was in the first year and I didn't do too well. I ...
173 views

### Not sure what a student is misunderstanding on this Stat question

Here is the solution I presented: (a) P(G|B) = (5/24) * (.125) = .026. Since you select ONE senior manager, then P(B) is 4/23. Now, if we are dealing with a second employee who is also a senior ...
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### 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 ...
233 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 ...
14k 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 ...
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1 vote
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### 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 ...
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### Transition into a non-explicit sample space world

This is one of the problem taunting me over years while explaining probability. In most of the high-school as well as graduate textbooks, there are at most very few lines to deal with this problem. ...
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### 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 ...
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### 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 ...
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### 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 ...
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 ...
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### 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 ...
93 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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### 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 ...
158 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 ...
208 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) \...
121 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 $X$ ...
160 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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### 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 ...
241 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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### 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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### 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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### 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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### 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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### 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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### 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. ...
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492 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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### 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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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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766 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. ...
105 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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