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Nayland College - Mathematics

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NZAMT NZQA NZ Grapher NZ Maths Census at School Study It Khan Academy Desmos

Probability Introduction

2.12 Probability HOME | Objectives | Probability Review | Probability tables | Two Way Tables | Risk & Relative Risk | Tree Diagrams | Conditional Prob | Distributions | Actual vs Normal | Normal Distribution | Inverse Normal | Revision


Probability review: Theoretical vs Experimental


Higher or lower card game

Monty Hall's Dilemma and animation - stay or switch

1) Interpreting risk and relative risk
2) Normal Distribution (and experimental distributions)
3) Two-way tables & Probability Trees

Basic concept of probability P(event)=
Experimental vs Theoretical
Long Run Relative Frequency
HTH, dice,

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


Class notes | Blank notes

Probability fair (link to

Simulating dice | 30 dice simulation

long run relative frequency

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)




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


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)


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



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