School level

# 1st April

## 1st April: Expected Value

### Learning Outcomes

Students studying at OL should be able to:

• calculate expected value and understand that this does not need to be one of the outcomes
• recognise the role of expected value in decision making and explore the issue of fair games
Workshop Resources & Presentations
Explanatory Videos
GeoGebra Files
SEC Exam Questions

### Expected Value

A presentation to introduce the concept of Expected Value and Fair Games to students. Expected value is calculated and students discover that that this not need be one of the outcomes. The issue of fair games and the role of expected value in decision making is explored.

SC Mathematics

#### How it maps to the curriculum

SC
Mathematics

Strand: 1. Statistics & Probability

Strand unit: 2. Concept of Probability

Suggestions for use: To introduce the concept of expected value and fair games to students

Asset type: Presentation
Language: English
Rights: Attribution-Noncommercial Share Alike Creative Commons
Special Needs:

### Modular Course 1 Module 4 Presentation

The fourth module of the probability and statistics course deals with more advanced concepts of probability pertaining to multiple events. The concepts of events which are mutually exclusive and events which are independent are discussed. The basic rules of probability for independent and non-independent events are presented and concepts of conditional probability are discussed. The use of Venn diagrams and probability trees when solving multiple-event problems is presented.

SC Mathematics

#### How it maps to the curriculum

SC
Mathematics

Strand: 1. Statistics & Probability

Strand unit: 2. Concept of Probability

Suggestions for use: Teacher planning guide

Asset type: Presentation
Language: English
Special Needs:

### Modular Course 1 Module 4 Notes

The fourth module of the probability and statistics course deals with more advanced concepts of probability pertaining to multiple events. The concepts of events which are mutually exclusive and events which are independent are discussed. The basic rules of probability for independent and non-independent events are presented and concepts of conditional probability are discussed. The use of Venn diagrams and probability trees when solving multiple-event problems is presented.

SC Mathematics

#### How it maps to the curriculum

SC
Mathematics

Strand: 1. Statistics & Probability

Strand unit: 2. Concept of Probability

Asset type: Document
Language: English
Special Needs:

### Modular Course 1 Module 4 Activities

Activities & Problems from Module 4

SC Mathematics

#### How it maps to the curriculum

SC
Mathematics

Strand: 1. Statistics & Probability

Strand unit: 3. Outcomes of Random Process

Suggestions for use: Teacher resource to be used with Modular Course 1 Module 4 presentation.

Asset type: Document
Language: English
Special Needs:

### Modular Course 1 Module 4 Activity Solutions

Solutions to Module 4 Activities

SC Mathematics

#### How it maps to the curriculum

SC
Mathematics

Strand: 1. Statistics & Probability

Strand unit: 2. Concept of Probability

Asset type: Document
Language: English
Special Needs:

### Project Maths Workshop 10 Notes

Workshop 10 focused on the importance of using a variety of approaches and strategies when teaching and learning mathematics.Time was spent discussing inferential statistics and in particular deferred material which will be examined for Leaving Cert. 2015. Activities on problem-solving and an overview of the process of lesson study were also gone through on the day. If you missed workshop 10 or want to go back over some of the activities done on the day, you’ll find videos of the full workshop and all the resources used or references during the workshop below.You will find all resources used in workshop 7 here including videos of the full day.

SC Mathematics

#### How it maps to the curriculum

SC
Mathematics

Strand: 1. Statistics & Probability

Strand unit: 2. Concept of Probability

Asset type: Document
Special Needs:

### Tossing Coins - Plan

In this Teaching & Learning plan students learn that by tossing two coins and observing the results (two heads, two tails, one head and one tail) not all results are equally likely. They relate the number of outcomes to the fundamental principle of counting, determine the probability of an event using the results of an experiment and use this to predict the result of a repetition of the experiment, for
equally likely outcomes. The term ‘independent events’ is introduced.

SC Mathematics
JC Mathematics

#### How it maps to the curriculum

SC
Mathematics

Strand: 1. Statistics & Probability

Strand unit: 3. Outcomes of Random Process

Suggestions for use: Students learn that by tossing two coins and observing the results (two heads,
two tails, one head and one tail) not all results are equally likely.

JC
Mathematics

Strand: 5. Statistics and Probability

Strand unit: 1. Chance Experiments

Suggestions for use: Students learn that by tossing two coins and observing the results (two heads,
two tails, one head and one tail) not all results are equally likely.

Asset type: Document
Language: English
Rights: Attribution-Noncommercial Share Alike Creative Commons
Special Needs:

### Project Maths Workshop 10 Video

Workshop 10 focused on the importance of using a variety of approaches and strategies when teaching and learning mathematics.

SC Mathematics

#### How it maps to the curriculum

SC
Mathematics

Strand: 1. Statistics & Probability

Strand unit: 2. Concept of Probability

Asset type: Video
Language: English
Special Needs:

### Introduction to Expected Value

Khan Academy introductory video explaining how to find expected value.

SC Mathematics

#### How it maps to the curriculum

SC
Mathematics

Strand: 1. Statistics & Probability

Strand unit: 2. Concept of Probability

Asset type: Video
Language: English
Special Needs:

### Spinner and expected value

https://www.geogebra.org/m/B2CpLd0Z Added: 31 Mar 2020 Contributor: PDST Resource type: App/software

GeoGebra file to explore how expected value is related to the mean value

SC Mathematics

#### How it maps to the curriculum

SC
Mathematics

Strand: 1. Statistics & Probability

Strand unit: 2. Concept of Probability

Asset type: Online Resource
Language: English
Special Needs:

### Calculate expected value

https://www.geogebra.org/m/hPS3vHzZ Added: 31 Mar 2020 Contributor: PDST Resource type: App/software

GeoGebra file to calculate the expected value of the random variable X for the given probability distribution.

SC Mathematics

#### How it maps to the curriculum

SC
Mathematics

Strand: 1. Statistics & Probability

Strand unit: 2. Concept of Probability

Asset type: App
Language: English
Special Needs:

### Deal or no deal

https://www.scoilnet.ieuploads/resources/32403/32145.xls Added: 31 Mar 2020 Contributor: PDST Resource type: Game / Simulation

Excel file allowing students to play the game 'deal or no deal' to deepen understanding of expected value

SC Mathematics

#### How it maps to the curriculum

SC
Mathematics

Strand: 1. Statistics & Probability

Strand unit: 2. Concept of Probability

Asset type: App
Language: English
Special Needs:

### OL 2018 P2 Q3

SEC Question on expected value

SC Mathematics

#### How it maps to the curriculum

SC
Mathematics

Strand: 1. Statistics & Probability

Strand unit: 2. Concept of Probability

Asset type: Document
Language: English
Special Needs:

### OL 2014 Sample P2 Q2

SEC Question on Expected Value

SC Mathematics

#### How it maps to the curriculum

SC
Mathematics

Strand: 1. Statistics & Probability

Strand unit: 2. Concept of Probability

Asset type: Document
Language: English
Special Needs:

### 2013 P2 Q2

SEC Question on expected value

SC Mathematics

#### How it maps to the curriculum

SC
Mathematics

Strand: 1. Statistics & Probability

Strand unit: 2. Concept of Probability

Asset type: Document
Language: English
Special Needs:

### HL 2016 P2 Q6

SE question on expected value

SC Mathematics

#### How it maps to the curriculum

SC
Mathematics

Strand: 1. Statistics & Probability

Strand unit: 2. Concept of Probability

Asset type: Document
Language: English
Special Needs:

### 2014 P2 Q5

SEC question on expected value

SC Mathematics

#### How it maps to the curriculum

SC
Mathematics

Strand: 1. Statistics & Probability

Strand unit: 2. Concept of Probability

Asset type: Document
Language: English
Special Needs:

### HL 2013 P1 Q1

SEC question on expected value

SC Mathematics

#### How it maps to the curriculum

SC
Mathematics

Strand: 1. Statistics & Probability

Strand unit: 2. Concept of Probability

Asset type: Document
Language: English
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