Questions tagged [probability]
For questions about the teaching of probability, dealing with students misconceptions in probability, and explaining probability theory paradoxes.
74 questions
8 votes
2 answers
241 views
Why do students misuse and misunderstand the terms "or", as well as "and" in probability?
I'm an instructor for an intro to stats course, where I handle the classes with active learning components/exercises. I've noticed, both in class and in office hours, is a very pervasive ...
- 233
7 votes
6 answers
588 views
The point of exercises on events or random variables independence
We teach our students that two events $A$ and $B$ are independent if $\Pr[A\cap B] = \Pr[A]Pr[B]$. Then, we often propose exercises of the form: "Prove that these two events are independent",...
- 171
1 vote
3 answers
468 views
Why can't I teach that picking (un)popular integers doesn't lower Probability of winning lotteries?
Every year at my secondary school, some student always insists that "picking unpopular numbers" lowers your probability of winning lotteries, as follows. Presuppose that lotteries let ...
- 31
6 votes
2 answers
405 views
The easy and the hard problems involving independent events
In probability, two events are independent if the incidence of one event does not affect the probability of the other event. Math textbooks often have a problem checking if two events are independent ...
- 161
3 votes
2 answers
448 views
Correct notation of a Sample space
From the very beginning I have used the notation $ S = \{ H , T \} $ as the Sample space for tossing a coin once and $ S = \{ HH , HT , TH , TT \} $ in the case of tossing a coin twice.I have several ...
- 1,242
0 votes
1 answer
129 views
Markov chains - how to translate mathematically the fact that the state at $n+1$ only depends on the state at $n$? [closed]
In a Markov chain of, say, three states $1,2,3$, when proving that the probabilistic state at $n+1$ ($\pi_n$) is equal to the probabilistic state at $n$ times the transition matrix, one has to use the ...
- 437
2 votes
3 answers
324 views
How to prove, without the LOTUS formula, to student that $V[aX+b]= a^2 V[X]$?
The mainstream way to show $V[aX+b]= a^2 V[X]$ is by using LOTUS. However, LOTUS seems to me too powerful and out-of-reach for a last-year high-school student. Therefore I was wondering if we could ...
- 437
-3 votes
1 answer
279 views
Does some textbook on probability use a particular way (described here) of accomplishing the segue into continuous distributions?
Imagine an introductory probability course that assumes the students have had first-year calculus and understand mathematical reasoning. At some point in such a course has explicated several families ...
- 2,288
6 votes
7 answers
2k views
Should I choose Cox-based Jaynes' approach or Kolmogorov approach to base myself on to teach probabilities to high-school students?
I am planning to become a math high-school teacher and have the following question: What Probability Theory should I base myself on to teach probabilities to students ? The classical approach is via ...
- 437
7 votes
7 answers
1k views
Special topics for introductory probability
I am helping to design a low-level college course whose purpose is to teach critical thinking, logic, finance and probability. I have been tasked with developing the probability section. I am ...
- 173
-6 votes
1 answer
153 views
PROBABILITY QUESTION [closed]
How to solve this probability question?f a, b, and c are in the range [0, 1], what is the probability that the quadratic equation ax^2 + bx + c has real solutions? justify your answer! This question ...
- 2,652
1 vote
2 answers
668 views
Online Probability Simulation for Compound Events
I'm teaching Grade 9 Probability. We need to compare Experiment Probabilities (Relative Frequencies) with Theoretical Probabilities for Simple and Compound Events. I want to come up with and Online ...
- 1,145
0 votes
1 answer
85 views
Seeking References on Deterministic and Stochastic Phenomena Suitable for High School Students
Can anyone recommend good and didactic references that delve into the dualism between deterministic and stochastic phenomena? Ideally, I'm seeking materials that provide a conceptual explanation along ...
- 2,652
1 vote
1 answer
129 views
Discrete Probability Modeling with Desmos or Spreadsheets
In my Finite Math course* almost every section includes a part where students have to create a file (from scratch) in Desmos or in Google Sheets. For example, they use Desmos to plot piecewise linear ...
- 8,434
6 votes
1 answer
1k views
Law of large numbers as a middle school topic?
My daughter (a biologist) is presently teaching also math at a middle school (9th grade, so about 14 years olds). Now the topic in probability seems to be the law of large numbers! More and more I ...
- 1,878