AS 3.3 Probability

1

Overview

Introduction, Lesson Sequence Definitions, Review of level 2 Probability, Probabilities from tables

Monty's Dilemma – Investigate probabilities of sticking with a decision, or switching.

Assessment Criteria | MR notes, Blank notes

Ex 6.01

Relative Frequency | Experimental prob | Simple probabilty

Achieving in Statistics (AIS) p47

2

Venn Diagrams

Introduction to Venn Diagrams and understanding concepts of: Union, Intersection, Complement, Mutually exclusive, Independence

Venn Diagrams – Investigate common features of sets.

MR notes, Blank notes
Mr Venn (pdf)

Ex 6.02 |Ex 6.03

AIS p48, 49

Venn Diagram Practice

Using Venn Diagrams to solve problems.

MR notes, Blank notes

p111 Ex 6.04A | 6.04B

4

Probability trees

Review of Probability Trees, and using probability trees to solve problems with & without replacement.

MR notes, Blank notes

p116 Ex 6.05A | 6.05B

Tree Diagrams

AIS p48

Probability tree practice

Solving problems using Probability Trees. Probability trees with Sum to Infinity.

Expected Value

A comparison of Discrete Random Variables and Continuous Random Variables. Introduction of the Expected Value, and how to calculate it.

MR notes, Blank notes

p121 Ex 7.01     p123 Ex 7.02

Expected Value practice

Practice finding the expected value and Application problems.

  p126 Ex 7.03A | 7.03B

Expected value when adding & multiplying

Finding the expected value when data  sets are multiplied and/or added to. The concept of E(Ax + B). Calculating E(x²)

MR notes, Blank notes

p130 Ex 7.04

Standard deviation & Variance

 Review of Standard Deviation and Introduction to Variance. Calculation of Variance & Applications.

MR notes, Blank notes

p135 Ex 7.05    p137 Ex 7.06

Variance when adding & multiplying

Calculating the Variance when data sets are multiplied and/or added to. The concept of Var(Ax + B)

MR notes, Blank notes

p138 Ex 7.07A | 7.07B

  AIS p65

Adding two populations

Calculating the Variance when several data sets are combined: Var(X ± Y).

And when several data sets are scaled then combined. The concept of Var(AX ± BY).

Understanding the difference between Adding and Multiplying variables: Var( Y + Y + Y) ≠ Var(3Y)

MR notes, Blank notes
practice examples: MR notes, Blank notes

p143 Ex 7.09 | p145 Ex 7.10

A revision Assignment

Factorials

Basic Arrangements & Selections from different groups. Factorial notation!

MR notes, Blank notes

 p147 p150 Ex 8.01

Permutations

Understanding and calculating Permutations ⁿP_r (selecting 'r' items from a group of 'n' items when order is important)

  MR notes, Blank notes

p154 Ex 8.02A | 8.02B

Combinations

Understanding and calculating Combinations ⁿC_r (selecting 'r' items from a group of 'n' items when order is not important)

MR notes, Blank notes

p159 Ex 8.03A | 8.03B

Arrangements & Probabilities 

Calculating Probabilities which involve Arrangements (Permutations & Combinations)

MR notes, Blank notes , More examples

p161 Ex 8.04A | 8.04B

Practice

Further practice of mixed problems Probabilities which involve Arrangements. Excellence problems and Factorial proofs.

Factorial proofs: MR notes, Blank notes

p164 Ex 8.05A | 8.05B

Conditional Probability

Introduction to and problems involving Conditional Probability.

MR notes, Blank notes

p167 Ex 9.01     p169 Ex 9.02

Conditional Probability

AIS p54,55,56

Mixed Problems

Practice of mixed Conditional Probability problems.

 Practice of all Mixed Problems & Revision

Summary of probability

p178 Ex 9.05A | 9.05B

Practice test paper | Solutions

Probability Jeopardy PowerPoint

Worked solutions to Mr Popes Revision Sheets POPES 3.3 Probability revision sheets:
1 2 3 4 5 6 7 8 9 10

Exam Paper revision