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Nayland College - Mathematics

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NZAMT NZQA NZ Grapher NZ Maths Census at School Study It

3.13 Probability HOME | Achievement Objectives | Overview | Vocabulary | Expected value | Venn Diagrams | Union, Mutually exclusive, Complement | Independence | Conditional | Tree Diagrams | Risk & Relative risk | Simulations | Revision

AS 3.13 Overview



Higher or lower card game

Monty Hall's Dilemma and animation - stay or switch

Review of Theoretical vs Experiential probabilities

6 sided dice simulation and a 6 to 30 sided dice

The number of repeats required to get a probability estimate when drawing coloured balls from a box How many of each colour?(up to 3000 trials)

Concept: How many trials before the experimental probability is close to the actual probability?

How stats fool juries - Peter Donnelly

Nice clear videos by Brandon Foltz. Discrete Random Variable

Class notes pdf
Class Handout (print version)
Class site


6 sided dice simulation:

pg 63 - 65



Concept: long run relative frequency Coin flipping 1-500 flips (allow macros) How the relative frequency graph varies but ends up very similar

Concept: that randomness is not smooth
Random scatter plot, Random plotting points
Random coin flip vs made up one Random coin flips H T T H T T H H...
Coin Toss interactive (

Are students familiar with randomness?

Class notes pdf
Class Handout (print version)

Random plotting points:

Khan Academy video on basic Probability


Probability review

Probability describes how likely an event is to occur

Probabilities can be calculated (theory) or recorded (practical) or simulated (using random number generator)


As more trials are done the probability becomes more accurate


Expected value E(x) = probability x Number of trials

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Equally likely outcomes

A normal 6 sided die is rolled.


P(multiple of 3)=
P(less than 5)=
P(at least 2)=
P(not a 2)=

Mouse-over key words


Long run relative frequency

Flipping a coin:

10 trials

100 trials

500 trials

Mouse-over key words


Relative frequency equals the probability

Note: as the number of trials increases the relative frequency levels off at 0.5 (as expected)

Excel coin flipping simulation  |  Excel coloured ball simulation


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