Probability can range in from 0 to 1, where 0 means the event to be an impossible one and 1 indicates a certain event. Submit a Proposal. Ib maths tutor at

Topic 3: Geometry & Trigonometry. Applications. If m = p qwherepand qare prime, (m) = ( p 1) (q 1) and this is what we called A .in the description of the RSA algorithm. Learning With Mr. DeAbreu Probability. blackburn central 100 front light; northern nights drive-in lancaster nh; compare offset mortgages; designing a football stadium. Page updated. Statistics and Probability is Topic 4 in both of the new IB math courses, Applications and Interpretation and Analysis and Approaches. This webinar focuses on the changes to Statistics and Probability within the new courses and will help prepare you with resources to teach this topic. Topic 4: Statistics. Compares results and reflects on this. Check out the list below for enticing topics to write about: Our specialists will write a custom essay. HOME; ABOUT; TESTIMONIALS; SERVICES; CONTACT US Quienes somos; Servicio de Soporte; Llmanos al 622793100; Inicio; Desarrollo web. Original: Source. The additional content for HL consists of Bayes" theorem and further material on discrete & contrinuous random variables. Words: 892; Pages: 3; Preview; Full text; 18 The Mathematical Exploration Internal Assessment List of 200 ideas/topics for a Mathematical Exploration The topics listed here range from fairly broad to quite narrow in scope. Suitable for Applications and Interpretations students (SL and HL) and also Analysis Average IAs - Examples; Probability Using Baye's Theorem and Binomial Theorem Analysis: Baye's Theorem and Baseball IB Maths HL IA Tutors; IB Maths SL IA Tutors; IB Maths Studies IA Tutors; IB Maths Notes. Application deadline: April 8 Location: Washington, DC (American University) Topics: Students will participate in research seminars in mathematics, probability and statistics in which research projects will be investigated in teams. math ia probability examples. Download & View Ib Math Sl Ia Topics as PDF for free.

IB Mathematical Studies Internal Assessment: Shoe Size versus Length of Forearms Exam Session: May 2012 School Name: International School Bangkok IB Number: 000307-161 Teacher: Ms. Goghar Date: January 20, 2012 Course: IB Math Studies SL Word Count: 2,338 Name: Jennifer Purgill. Triangle Relationships. 1670+ Video tutorials, 1227+ PDF IB Resources, 195+ Sample IAs, 148+ EEs, 8777+ Sample questions, 653+ quizzes, IB Math solutions - explore ib resources. Many events cannot be predicted with total certainty.

The probability of head each time you toss the coin is 1/2. CHAPTER 8, 10, 3, 15 - OXFORD MATHEMATICS STANDARD LEVEL 3.3-3.5 Sample space diagrams, product rule, conditional probability, tree diagrams. Revision Village - Voted #1 IB Maths HL Resource in 2018/19! Topics include Algebra and Number (proof), Geometry, Calculus, Statistics and Probability, Physics, and links with other subjects. IB Maths AA Tutors; IB Maths AI Tutor; IB Maths IA Tutor. Math IA : Exemplary IAs - Examples. Direct video links allow a teacher to grab and include a clip, for example into a presentation. More details. My area of interest lies in probability; therefore, I explored various topics based around that. Scroll down this page to find over 300 examples of maths IA exploration topics and ideas for IB mathematics students doing their internal assessment (IA) coursework. Topics include Algebra and Number (proof), Geometry, Calculus, Statistics and Probability, Physics, and links with other subjects. You need to make sure that you attempt the IB math essay because you are interested in the study. More Resources You can, of course, choose other topics that meet your requirements. When you choose a topic that is genuinely of interest to you, it reflects in the final outcome. So Eulers theorem implies that M A 1 mod m. Using to mean has the same remainder when divided by m and remembering the The formula for deciphering is M = CD (modulo m) C ME. worksheets.

The hyperboloid shape of a nuclear Natural Draft Cooling Tower - Model the shape, find the airflow metrics, calculate the volume and surface area. If AI is the secret sauce to make Pepper smarter! Jan 28, 2018 Also, I have an idea to do a maths IA analysing the patterns in music with the composers, what type of statistics would be useful? Ask the students to spin the spinner 10 times. The topics covered in this section will be: Topic 5: Calculus. Prerequisites: of ways A can occur)/(Total no. The Solution. In this article, we have compiled a list of 22 topics you can choose for the International Baccalaureate standard level Math Internal Assessment. As an extensi [Show more] On math I learned about probability. However, using the strategies outlined in this book, he was able to receive a solid 7 on his Math IA. All you need is the right preparation, the proven tactics, and a mindset shift. The Analysis & Approaches courses both have five core topics that both SL and HL students study (for different amounts of time): Topic 1: Number and Algebra. 1 Introduction The Mathematical Tripos consists of Parts IA, IB and II, taken in successive years, with an optional fourth year, Part III, taken by students who do suciently well. Maths AI for students interested in social sciences, natural sciences, medicine, statistics, business, engineering, some economics, psychology, and design.

Essential list of math topics for Machine Learning and Deep Learning. 100 Units. Looking for your Lagunita course? Introduction to Probability (3-0) Cr. What is ALEKS? worksheet generators. View -Math IA Outline.pdf from MATH 3320 at Texas A&M University, Kingsville. Each team will write a final paper discussing their results and give an oral presentation. extras. Then scale it on geogebra and take note of the coordinates. Also you can come in and look at the HL math textbook that has a section on the IA and includes a list of 200 possible topics many of which would also be appropriate for an SL math student Review of multilevel cache memory and their energy For example, if you want to come up with the balance sheet of a company, you will Get Probability For Class 10 at BYJUS. The application of probability can be seen in Maths as well as in day to day life. It is necessary to learn the basics of this concept. The questions here will cover the basics as well as the hard level problems for all levels of students. Thus, students will be confident in solving problems based on it. of possible outcomes) Another example is the rolling of dice. 15.3 The normal distibution. Thanks guys!. IB Tuition Tutors - We offer Ib Math Ia Ai Topics in Mumbai, Maharashtra. Introduction to residuals and least squares regression. IB Mathematics HL IA Sample On Use Of Mathematics In Coding While Encryption Or Decryption. Hundreds of IB Math AA SL Questions with Video Explanations sorted by topic, sub-topic, and difficulty. What Makes a Good Math IA Topic Rock Rapids, IA 51246-1759 800-622-3070 www Now the C(n,2) comes from the pairs (two people having the same birthday) Computer Black Screen Loud Fan Reddit probability is P(B IA), read as the probability of B given A probability is P(B IA), read as the probability of B given A. Plotting Log graphs of planetary patterns. Then I derived formula and calculated how long it would take to crack passwords of different strengths. Statistics. the grounds mobile, al concerts; birmingham city kit 2021/22. This is important to point out that as the probable topics for maths IAs are so vast that each topic of maths IA would be addressed differently, this blog will disseminate the top 20 IB maths IA topics along with the comprehensive advice as opposed to necessary components of each IA; which can be otherwise be inferred from the IA marking criteria. The first thing our math teacher (which is also our ib coordinator) told us about the IAs is to not do any game theories like poker, card games etc. Answer: These are topics for an IA exploration in Statitics: Statistics and modelling 1) Traffic flow: How maths can model traffic on the roads. If you have ISU Mathematics related questions about ALEKS please email ejstines@iastate.edu.You can expect a response within 48 hours. Methods to solve simultaneous equations. Maths IA Maths Exploration Topics: Scroll down this page to find over 300 examples of maths IA exploration topics and ideas for IB mathematics students doing their internal assessment (IA) coursework. ( Original post by Dotti22) Hi Everyone, For my Maths IA I wanted to look at the probability of winning a tennis game. the English mathematician Lewis Fry Richardson was researching the correlation between shared border length and the probability of war among two adjacent countries. 1. Learn more. Pascals triangle patterns: Fibonacci sequence. Choosing the topic is usually the trickiest part which many IB students struggle with. Ideas for Probability Projects for Math. Probability projects in math means bringing out the dice, the spinners and the playing cards. These tools are all ways to determine the possible occurrence of a future event, compared to the chance of its nonoccurence--or probability--according to John Van De Walle, "Teaching Elementary and Middle School The permutations and combinations of a rubics cube. 4. How is it

Topics include Algebra and Number (proof), Geometry, Calculus, Statistics and Probability, Physics, and links with other subjects. Math IA : Below Average IAs- Examples. how likely they are to happen, using it. Topic 5: Calculus. interdisciplinary exams. More Topics. Topic 5 - Probability & Statistics. 3. Math AA: Math AI: Focus area-Emphasis on algebraic methods: Focus area-Modelling and Statistics: Aims and objectives-Develop strong skills in mathematical thinking: Aims and objectives-Develops strong skills in applying practical mathematical problems to the real-worldDeals with-Mathematical problem and exploring real and abstract applications: Deals Topics include: program structures, expressions, variables, decision and logic, iteration, collections, input, and output. You can contact us via our email or by filling out the contact form in our site. IB Mathematics HL. A specific emphasis will be on the statistical and decision-theoretic modeling paradigm. Annotated: Probability in Courtroom Modeling Microwave Popcorn 1. Find here details about our company including contact && address| ID:23571438155. 4 yr. ago. Once you have passed the trials of basic math, you can move on to the advanced section. Search: Probability Math Ia Sample. The origins of Greek symbols in mathematics. 2) Logistic function and constrained growth 3) Benfords Law using statistics to catch criminals by making use of Through online courses, graduate and professional certificates, advanced degrees, executive education #2. regents exams. Answer (1 of 5): You can do a math investigation on anything that has applications that are slightly out of the reach of the IB math course you are taking. Basic formula of probability. More Math Exploration Topics. IB Mathematical Studies Internal Assessment: Shoe Size versus Length of Forearms Exam Session: May 2012 School Name: International School Bangkok IB Number: 000307-161 Teacher: Ms. Goghar Date: January 20, 2012 Course: IB Math Studies SL Word Count: 2,338 Name: Jennifer Purgill. The Geometry of Antoni Gaudi. Even though many of these topics led to high scores for some of our graduates in the past, it is important that you listen to the advice of your subject teacher before choosing any topic! Scroll down this page to find over 300 examplesof maths IA exploration topics and ideas for IB mathematics students doing their internal assessment (IA) coursework. Prereq: Credit or Enrollment in MATH 140 or higher Introduction to computer programming with an emphasis on problem-solving. Programming assignments including games and applications. Revision Village - Voted #1 IB Maths HL Resource in 2018/19! Bayes Thorem and the Probability of Inaccurate Diagnosis in 40-89 Year-Old Individuals in Relation to the Excess Healthcare Burden of Osteoporosis in the United Kingdom. This area includes topology, combinatorics, logic, and computational mathematics. IB Mathematics SL Internal Assessment Shaikha AlArayedh Mr. Antoine Fayad 000707-0003 May 2014 & & & & & & & & & & & & & & & & & 1& Introduction From the stimulus sports I chose to centre my internal assessment on basketball. If time permits, have them spin it 100 times. Probability. P (E 2) = 275/500 = 0.55. Edited March 6, 2013 by So is the probability of tail. Probability is a measure of the likelihood of an event to occur. More Resources Calculating the equation of a regression line. It shocked me since there are

T he language and vocabulary of mathematics contain a large amount of symbols some being more technical than others. Math 8. Textbooks for Analysis & Approaches and Applications & Interpretation. Choosing an IB Math IA Topic. The final grade was a 7 (18/20). The probability of a coin landing on heads twice in a row is a compound probability that is computed as the product of the probabilities of the independent events, or: 0.5 0.5 = 0.25

Math 9E. The Sum of probabilities of all elementary events of a random experiment is 1. 507 Words. Most baseball players do not look at the math behind the performance. So you take 1 (total sample space) - P (not your birthday) = P (share your birthday) Because P (A) = 1- not (P (A)). Topic 3: Geometry & Trigonometry. Newest IAs: #1: Latvian Dancing #2: Modelling Space Debris #3: Arthur wasnt the best at Math; he received a Worked example using least squares regression output. Now that we have some basics out of the way, here are some IB Math IA topics ideas: Pascals triangle: looking into the patterns of the array of numbers. Ia Math. Math 10S Math 6. Topics include Algebra and Number (proof), Geometry, Calculus, Statistics and Probability, Physics, and links with other subjects. 15.2 The binomial distribution. Symmetry and the Curve. Thus 364/365 is the prob of not (P (A)). Topic 2: Functions. (Mustgo beyond a simple 50% win probability for each game.) These fields have power and limitations and should be applied with care and critically questioned, in detail, to differentiate between the theoretical and the empirical/observed. Stanford Online offers a lifetime of learning opportunities on campus and beyond. Model musical chords and musical concepts such as dissonance. Topic 3: Geometry and Trigonometry. regents exam archives 1866-now. IA Maths SL 6. Fast and easy to use Statistics & Probability. Find the surface area/volume of an egg. 2020 Absolute Value Addition Problem. Mathematics in Movies. Counting methods, elementary probability and statistics. Make sure you go to kognity to answer the questions. Program dates: June 5 - July 23. 23 Avr. 05 Mar. Find a curved road on google earth, copy it. Honors Calculus I. P-Value: The p-value is the level of marginal significance within a statistical hypothesis test representing the probability of the occurrence of a given event. IB Maths HL IA Tutors; IB Maths SL IA Tutors; IB Maths Studies IA Tutors; IB Maths Notes. 1) Traffic flow : How maths can model traffic on the roads. Filter exemplars. I learned the experiment, sample space and event. Considers modelling. Expressions of Power. Pascals triangle: Discovering patterns within this famous array of numbers; Pythagorean triples: Can you find patterns in what numbers form a pythagorean triple? That could be something you might to consider as well. A list with over 300 examples of maths IA exploration topics and ideas for IB mathematics students doing their internal assessment (IA) coursework Matrix multiplication is associative A frequency table is constructed by arranging collected data values in ascending order of magnitude with their corresponding frequencies Members in the group are Hundreds of IB Math AA SL Questions with Video Explanations sorted by topic, sub-topic, and difficulty. After research I was startled to find that in a room of just 23 people, there is a 50-50 chance of two people sharing a birthday. P (all Y) = .24 12 6 12 6 3 3 1 = (2 1 ) 3 3 1 = 1 24. Words: 892; Pages: 3; Preview; Full text; 18 The Mathematical Exploration Internal Assessment List of 200 ideas/topics for a Mathematical Exploration The topics listed here range from fairly broad to quite narrow in scope. Statistics is a form of mathematical analysis that uses quantified models, representations and synopses for a given set of experimental data or real-life studies. Monty 15.1 Random variables.

The site has changed in 2010 from Flash to HTML5 video. Desarrollo tiendas online; Soluciones tecnolgicas para tu tienda online Animals and Pets Anime Art Cars and Motor Vehicles Crafts and DIY Culture, Race, Hey guys so I think I want to do my math ia on probability, more specifically probability in the health care industry. The Solution. Now the C (n,2) comes from the pairs (two people having the same birthday) Additional topics selected from probability, algebraic combinatorics, and applications. MATH 16100-16200-16300 is an honors version of MATH 15100-15200-15300.

Photo by Alex Knight on Unsplash. 200 Potential Topics. C4Engaged with the Mathematics in a topic obviously relevant to herself and uses real-life data. Math IA : Below Average IAs- Examples. [2019 Updated] IB Maths HL Mini Topic Exam > Statistics & Probability. A place for all users to find information related to the Math IAs. About Math Probability Ia Sample . Where should the kicker kick it Which way should the goalie dive Now you find the function of best fit. Calculating residual example. This is a collection of movie clips in which Mathematics appears. Stop searching. 02 Mar. So talk to your professor, maybe this was just my professor but make sure it is a safe choice :) 1. level 1. Circle C1 has center O and radius r. Circle C2 has center P and radius OP. 1-10. These characters and their fates raised many of the same issues now discussed in the ethics of artificial intelligence.. Real-world applications of the theorem of Pythagoras. A com brings you a greater love of mathematics, both for its beauty and its power to help solve everyday problems For the entire sample space; P(S) = 1 Our grade 2 fraction worksheets introduce students to fractions as both parts of a whole and parts of a set The Search: Math Ia Examples Statistics. F.S.SS.

MATH 314: Graph Theory (3-0) Cr. Discrete probability distributions so there are 364 days that are not your birthday, and the total number of days is 365. yordenis ugas vs crawford. Suitable for Applications and Interpretations students (SL and HL) and also Analysis and Approaches students (SL and HL). Report 4 years ago. It started during spring break 2006 (almost 16 years now). 2. 1. However, to make this more specific I wanted to focus on the rivalry between Nadal and Federer and use historical information (from their previous matches) to determine who would win in what conditions. for $13.00$10.40/page. P (E 3) = 120/500 = 0.24. get all child elements javascript Commentaires ferms sur urbantrail-lausanne.com FAIT PEAU NEUVE. IA Math AA HL 5. ri ( pr-r, pr-r) adj probability is P(B IA), read as the probability of B given A Copy and complete the probability tree diagram below . Which is closest to the length of the side of the square? The p 20 Math Internal Assessment Topic Ideas for SL Students. Proof that It works: Arthur wasnt the best at Math; he received a 28% on his mocks. The Statistics & Probability topic is the syllabus topic (out of 5) that has the least amount of HL content. to calculate a trend (predict life expectancy. IA Math AA HL 6. This course will introduce the basic ideas and techniques underlying the design of intelligent computer systems. Probability. over 300 examples of maths IA exploration topics and ideas for IB mathematics students doing their internal assessment (IA) coursework. If you are asking, what is a good topic for a Math IA, we can help you brainstorm. ~~~ In this IA, I determined the criteria of a strong password that cannot be easily broken by computer. In addition please join us on Wednesday, February 3, from 10:30a - 11:30a EST as Sarah Caban, Illustrative Mathematics Grade 5 Lead Author and Facilitator presents, Illustrative Mathematics K-5 Curriculum by Kendall Hunt  Axiomatic approach Axioms (countable case) More math is involved behind the scenes: combinatorics used in counting To calculate the probability that every single question would be answered with a yes, I had to multiply the numbers that in the path on the tree diagram that follow yes for each guess. 2.Probability of successful penalty kicks in a soccergame. Here is a list of 20 interesting topics to help you get inspiration: 1. A place for all users to find information related to the Math IAs. 2.

Topic 2: Functions. Find the next one and, if possible, the one after that 111, may be assigned to 111, may be assigned to.

You can contact us via our email or by filling out the contact form in our site. S. Prereq: MATH 166 or MATH 166H; MATH 201 or COM S 230 or CPR E 310 Structure and extremal properties of graphs. Search: Math Studies Ia Examples Statistics. Posted March 6, 2013 (edited) Check out hypergeometric. Basketball is Investigating the safe operating speed for ground vehicles on a given road segment. You can find past paper questions separated by topics for the modules below. See the Box "R-squared" if your want to assess the fit in least squared regression. Find resources which includes Sample Papers, Sample IAs, Samples EEs Distributed Among 115+ files which will act as your secret weapon to ace your IB Mathematics HL exam. 4) Bad maths in court - how a misuse of statistics in the courtroom can lead to devastating miscarriages of justice. Prerequisite: MATH 161 and EDUC 275, may be taken concurrently. Artificial beings with intelligence appeared as storytelling devices in antiquity, and have been common in fiction, as in Mary Shelley's Frankenstein or Karel apek's R.U.R. Be it IB SL Math IA topics or any other assessment or essay topic, whenever the topic is of your choice, it shows in the final outcome of the essay. Studying the concepts of Math is one thing, but interlinking the concepts with theory, abstract and evaluating a long report is an entirely different ball game. D3Considers other concentration time graphs. Download & View Ib Math Sl Ia Topics as PDF for free. Topic: probabilities and password cracking. Catalog Description. As you might know from the list of GMAT maths formulas, the Probability of the occurrence of an event A is defined as: P(A) = (No. No Tags | Non classNon class

More details. Math IA Outline Topic: Probability of Golf Putts Research Question: What is the probability of successful golf putts from Study Resources These results could provide an insight on a possible matchup between a player and an important opponent. com brings you a greater love of mathematics, both for its beauty and its power to help solve everyday problems So you take 1 (total sample space) - P(not your birthday) = P(share your birthday) Because P(A) = 1- not(P(A)) The content Common Pitfalls (Two units of credit offered for MATH 180A if ECON 120A previously, no credit offered if ECON FIND OUT MORE about mathematics courses and get answers to questions about Mathematics placement by checking the Mathematics section of the online course catalog.. 08 Dec. math hl ia statistics example. The May 2013 HL students did an IA on dice. There are 3 important things to consider when choosing the right course for you: Maths AA for students interested in mathematics, engineering, physical sciences, and some economics. We can predict only the chance of an event to occur i.e. ai lesson plans. screening for malignant neoplasm of breast icd-10 No credit if taken after MATH 76. So anything you find interesting. Month Hall problem: Looking into Bayesian probability work as a real-life scenario and add some sort of complexity to it. They see if their prediction is correct, after the first 10 spins. Maths Exploration (IA) ideas 23284 March 19, 2021 Predicting fire spread in wildlife fields : This mathematical model of fire presented in this paper offers for the first time a method for making the quantitative evaluation of both rates of spread and fire intensity in fuels that qualify for the assumptions made on the model. Then math is the air for all the essential ingredients to make that sauce! 3. fallacies in advertising examples Commentaires ferms sur CHANGEMENT DHORAIRE POUR LE DEPART LG ET LG RELAIS. All you need is the right preparation, the proven tactics, and a mindset shift. sleeper fantasy football cost. quick topics.

"/> MATH 104. MATH 676 Topics in Mathematics Credits: 3 (3-0-0) Explores unfamiliar maths and devises own approach to area under curve. Topic 1: Numbers & Algebra. regents books. 3. Good Essays. And then calculate the length of the function from point a to b. A student with a strong background in the problem-solving aspects of one-variable calculus may, by suitable achievement on the Calculus Accreditation Exam, be invited to register for MATH 16100-16200-16300. 2019 Exam LTAM, Long Term Actuarial Mathematics- Test is Taken on Campus in Iowa City, IA. Rationale/Introduction: The topic of my IA is birthday paradox. Topic 4: Statistics. Topic 1: Numbers & Algebra. Basic rules and axioms events, sample space, frequentist approach, dependent and independent events, conditional probability; 2. Matthew Steward on math-sl-ia-statistics-example. Modelling the shape of an Egg. \[ \begin{gather*}x \longrightarrow x+1 \longrightarrow (x+1)^2 \longrightarrow (x+1)^2 \ge 0 \\ \longrightarrow The data are represented by means of graphs. IA Task I Introduction and purpose of task: The purpose of this task is to investigate the positions of points in intersecting circles and to discover the various relationships between said circles.

Probability theory allows us to make informed choices, to evaluate risk and to make predictions about seemingly random events. The study of mechanical or "formal" reasoning began with philosophers and mathematicians in Analysis: Probability in Courtroom csafe. european cricket championship 2021 live score; david avanesyan next fight. romania eurovision 2010 Commentaires ferms sur math ia topics related to business. Like letters in the alphabet, they can be used to form words, phrases and sentences that would constitute a larger part of the mathematical lexicon. Is something like probability of catching coronavirus do able? 2. Free Printable Math Worksheets for Algebra 2 Created with Infinite Algebra 2. IA Math AA HL 6. The probability of the coin landing on heads on the first flip is 50%, and the probability of it landing on heads on the second flip is also 50%. Four textbooks written by Tim Garry and five highly experienced IB maths teachers (Wazir, Frederick, Nakamoto, Lumb & Landmann) provide comprehensive coverage for both of the new IBDP maths courses. Search: Probability Math Ia Sample. Math 10E. Therefore, the information could used by sports trainers to help players with performance enhancement. Topics in geometry include polygons, congruence and similarity, measurement, geometric transformations, coordinate geometry, and connections between numbers and geometry with selected applications. Models of Power. Create the worksheets you need with Infinite Algebra 2. IA Maths SL 6. Program construction and testing. The probability ratio will match the actual size of the spinner's sector the more times the spinner is spun. Ia Math. It involves probabilities in which there is no replacement. MATH 16100. After twirling the spinner 50 times students recheck their prediction. Birthday paradox was a topic that caught my interest the most. Google Sites. [2019 Updated] IB Maths HL Mini Topic Exam > Statistics & Probability. Those who successfully complete three years are eligible to graduate with a BA honours degree, while those who go on to complete the additional In order to find a function of best fit, look for polynomial regression. Calculus with Review IA. IB Maths IA examples. A place for all users to find information related to the Math IAs. Find the probability of each event to occur. The suggested teaching hours for SL is 27 hours and it"s only a few hours more for HL at 33 hours. IB Math IA Example 1670+ Video tutorials, 1227+ PDF IB Resources, 195+ Sample IAs, 148+ EEs, 8777+ Sample questions, 653+ quizzes, IB Math solutions - explore ib resources Prereq: Satisfactory performance on placement exam, 2 years of high school algebra, 1 year of high school geometry Permutations, combinations, probability, binomial and multinomial theorems, expected value, and applications.