DRV’s & Binomial Distribution

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AS Maths – Statistics – Probability Distributions

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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Download Slides

6A Slides (Courtesy of Owen134866)

Bicen Maths Live Lesson

Statistical Distributions 1 • Distributions and Binomial Probabilities • Stats1 Ex6A/B • 🎲

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths (Up to 4:45)

Download Blank Notes

(Courtesy of King’s Chester Maths Department)

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• Dr Frost Slides 1-11✦

Extra Questions

• Dr Frost Questions

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 547a: Determine the probability of a range from a discrete random variable.
• 547b: Determine unknown probabilities or connect probabilities in the probability distribution of a discrete random variable.
• 547c: Determine the probability of the sum of two or more outcomes from the same discrete random variable.
• 547d: Determine a probability using functional notation for the probability.
• 547e: Recognise situations under which the discrete uniform distribution is likely to be an appropriate model.
• 547f: Calculate probabilities using a discrete uniform distribution. (not yet active)
• 547g: Determine a constant in a function for a probability distribution.
• 547h: Determine two constants in a function for a probability distribution. (not yet active)
• 547i: Determine a probability using a probability function defined recursively. (not yet active)
• 547j: Determine the output of a cumulative distribution function given the probability function of a discrete random variable. (not yet active)
• 547k: Determine a cumulative distribution from a discrete random variable involving unknowns. (not yet active)
• 547l: Determine the probability of a range involving the coding of a discrete random variable with given distribution. (not yet active)
• 547: Exam Practice: Discrete random variables, including functional notation for probability distributions

Other Videos

Discrete Random Variables

Courtesy of Maths Genie

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Worksheets

• Naiker Maths
  • Probability Distributions: Exam Qs 2005–11✦ · Mark scheme✦
• SRWhitehouse
  • Discrete Random Variables Questions✦
• MadAsMaths (T. Madas)
  • Discrete Random Variables Q2, 5, 11, 12, 14, 19, 22–25, 33, 40, 41 (difficulty 2–5 of 5)

Old Spec Exam Qs

• PMT
  • Edexcel S1 Discrete random variables 1, Discrete Random Variables 2
  • OCR S1 Discrete Random Variables (Solutions)
  • OCR MEI DRV1 (Ans), DRV2 (Ans), DRV3 (Ans), DRV4 (Ans), DRV5 (Ans)

AS Maths – Statistics – Binomial Probability Introduction

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

Download Blank Notes

Download Slides

6B Slides (Courtesy of Owen134866)

Bicen Maths Live Lesson

Statistical Distributions 1 • Distributions and Binomial Probabilities • Stats1 Ex6A/B • 🎲

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths (From 4:45)

Download Blank Notes

(Courtesy of King’s Chester Maths Department)

Download Slides

• Dr Frost Slides 12-17✦

Extra Questions

• Dr Frost Questions

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 548a: Determine a binomial model appropriate for a given context.
• 548b: Determine the probability of no successes or all successes.
• 548c: Calculate binomial probabilities in the form P(X=x) (no context), and appreciate the relationship of this formula with the binomial expansion of (p + q)ⁿ
• 548d: Calculate binomial probabilities in the form P(X=x) in context.
• 548e: Know the assumptions made when modelling using a binomial distribution.
• 548: Exam Practice: Binomial distribution

Other Videos

The Binomial Probability Distribution

Courtesy of Maths Genie (Up to 3:49)

Binomial distributions | Probabilities of probabilities, part 1

3Blue1Brown Introduction to Binomial Distribution through Amazon Reviews

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Activities

• WW Introducing the Binomial Distribution Through Tree Diagrams PowerPoint
• Phet Online Falling Balls (link)
• Don Steward
  • Galton's Quincunx
• thewessens.net Classroom Apps
  • Binomial Bomber (simulate repeated binary events and watch the binomial distribution build up)
• BossMaths
  • Visualising the Binomial Distribution (Applet)
• MEI
  • Binomial experiment✦ (spreadsheet✦)
• SRWhitehouse
  • Binomial distribution (SRWhitehouse on TES)✦
  • Binomial distribution graphs✦

• Quincunx on mathsisfun.com Falling Balls (Similar to Above)
• Nrich Binomial or Not?
• Ben Sparkes Geogebra Binomial Distribution Explorer & Binomial Distribution

AS Maths – Statistics – Cumulative Binomial Probability

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

Download Blank Notes

Download Slides

6C Slides (Courtesy of Owen134866)

*WARNING, I do not use these slides exclusively as they do not refer to the use of a calculator. The Video is still good, but the example is it is different from the slides. My notes follow the slides, but I would obviously use a calculator rather than data tables to find any solutions.

Bicen Maths Live Lesson

Statistical Distributions 2 • Cumulative Probabilities for Binomial • Stats1 Ex6C • 🎲

Statistical Distributions 3 • Binomial within Binomial type question • Stats1 Ex6C • 🎲

Statistical Distributions 4 • Unknowns in Probability Range for Binomial • Stats1 Ex6C • 🎲

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths

Download Blank Notes

(Courtesy of King’s Chester Maths Department)

Download Slides

• Dr Frost Slides 18-23✦

Exam Practice

• Exam Practice

Extra Questions

• Dr Frost Questions

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 548f: Calculate cumulative binomial probabilities (no context).
• 548g: Calculate cumulative binomial probabilities in context.
• 548h: Calculate the probability of a range for a binomial distribution.
• 548i: Use a binomial probability to calculate another binomial probability.
• 548j: Determine the probability of success given the probability of at least one success.
• 548k: Determine the number of trials given the probability of at least one success.
• 548l: Use the probability of success obtained from a binomial distribution to find an unknown in a given function.
• 548m: Determine a range in a binomial model that leads to a given probability.
• 548n: Determine an unknown in a binomial distribution given a ratio between probabilities.
• 548: Exam Practice: Binomial distribution

Further Practice

• Practise Questions

Other Videos

The Binomial Probability Distribution

Courtesy of Maths Genie (From 3:49)

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Exam style Practice

• Naikermaths PPQs✦ (Solutions✦)
• Nrich ‘Over-Booking‘ Question
• PMT PPQs from Old Spec
  • AQA S1 Binomial Distribution
  • Edexcel S2 Discrete Distributions – Binomial 1, Binomial Distribution 2
• WW Nested Binomial Distribution Questions Word Doc or PDF

External Whole Topic Past Paper Style Questions

• WW Dr Frost Style QQQs (Version 1) Word Doc, PDF (Q’s Only) or PDF (Q’s & Sol.)
• WW Dr Frost Style QQQs (Version 2) Word Doc, PDF (Q’s Only) or PDF (Q’s & Sol.)
• Jethwa Maths Starter Activities (not p3-4)
• Mathsaurus PPQs (Video Solutions Pending)
• PMT Cheat Sheet
• Khan Academy
  • Sequence of Videos and Lessons with Practice Questions
• Standards Unit (DfES)
  • Standards Unit S8: Using Binomial Probabilities (Standards Unit, DfES; PDF

External Whole Topic Online Course

Worksheets

• Mathshelper (Jon Stone)
  • Binomial Questions
• MathedUp
  • Binomial Distribution: Questions · Challenge · Answers
• Maths Genie
  • Statistical Distributions: Questions · Solutions · Lesson · Topic page
• Mathsaurus (Kevin Olding)
  • Binomial distribution (exam questions)
• Physics & Maths Tutor
  • Binomial: Questions 2021–24 · Mark scheme · Model answers · Questions 2018–21 (with MS) · Model answers
  • Binomial (A-level papers): Questions 2021–24 · Mark scheme · Model answers
• MME
  • Appropriate Probability Distributions (AQA): Questions | Answers
• 1st Class Maths
  • Binomial exam-style questions✦ (answers✦)

Activities

• MEI
  • MEI teaching notes, misconceptions & prompts: Binomial distribution✦
• Dan Walker
  • S2 PowerPoints✦
• Andy Lutwyche
  • Erica’s Error’s On Statistical