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Tree Diagrams

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

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Probability Trees

Calculating probabilities from tree diagrams by multiplying along branches and adding between branches. Tree diagrams with and without replacement.

Intersection and Union problems

Tree diagrams

Class notes | Blank notes

Theta (new & old & workbook) Ex 22.02
NuLake EAS p135, 136

 

Overview

A tree diagram is a way of showing all possible options
(and probabilities) in a given situation

Explanation

Overview

Multiply along branches

Add between branches

Mouse-over above

Using a tree diagram to list all outcomes
Branches add to 1

 

 

With replacement

Select a card from a pack of 52 cards. Was it a heart? REPLACE the card and select a second card

Selection with replacement

Probabilities

P(2 hearts)=

P(1 heart)=

Mouse-over above

When items are selected and replaced, probabilities are CONSTANT.

 

 

 

Without replacement

Select a card from a pack of 52 cards. Was it a heart? KEEP the card and select a second card

Selection without replacement

Probabilities

P(2 hearts)=

P(1 heart)=

Mouse-over above

When items are selected and replaced, the probabilities CHANGE.

 

 

Example

Dodgy Dave's freight company sends 35% of packages 'standard' and the rest by 'express'
20% of 'standard' freight is lost
45% of 'express' freight is lost
What is the probability a package is lost?

Form a probability tree

Fill in known probabilities

Fill in other probabilities

Calculate
P(lost package)

Mouse-over above

 

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