7.01 Describing chance and sample spaces

What is probability?

Probability is all around us.

• There are the weekly Lotto and Powerball draws.
• Poker machines in clubs.
• Games that use dice, coins and cards.
• Weather events.
• Accidents and safety events.

The results of all of these are determined by probability - also called chance.

 

Sample Space

The sample space, sometimes called an event space, is a listing of all the possible outcomes that could arise from an experiment.

For example

• tossing a coin would have a sample space of $\left\{\text{Head},\text{Tail}\right\}${Head,Tail}, or $\left\{H,T\right\}${H,T}
• rolling a dice would have a sample space of $\left\{1,2,3,4,5,6\right\}${1,2,3,4,5,6}
• watching the weather could have a sample space of $\left\{\text{sunny},\text{cloudy},\text{rainy}\right\}${sunny,cloudy,rainy} or $\left\{\text{hot},\text{cold}\right\}${hot,cold}
• asking questions in a survey of favourite seasons could have a sample space of $\left\{\text{Summer},\text{Autumn},\text{Winter},\text{Spring}\right\}${Summer,Autumn,Winter,Spring}

Notice how the the sample space is listed inside curly brackets, with a comma between each outcome. 

 

Events

An event is the word used to describe a single result from within the sample space. It helps to identify which of the sample space outcomes we might be interested in.

For example, these are all events.

• Getting a tail when a coin is tossed.
• Rolling more than $3$3 when a die is rolled
• Getting an Ace when a card is pulled from a deck

We use the notation $P\left(\text{event}\right)$P(event) to describe the probability of a particular event.

 

Likelihood of an event

The likelihood of an event can be measured by a probability value. The probability values range between $0$0 (impossible) and $1$1 (certain).

 

Practice questions

QUESTION 1

QUESTION 2

Question 3