12.01 The language of probability

Describing probability

We often talk about the chance of something happening, or how likely something is to happen, to help us make decisions everyday. Probability is the chance of an event happening. We can describe this using words or numbers.

You may have heard people say, "That's impossible," or "I'll probably go to the shops tomorrow." These are words that describe the probability or chance of an event happening.

The probability of an event occurring ranges from $0$0 (impossible; it definitely won't happen) to $1$1 (certain; it definitely will happen). We can use fractions or decimals to describe probabilities in between, or even percentages. The diagram below shows how:

The probability of an event can lie anywhere in between $0$0 and $1$1. For example, a probability of $0.8$0.8 is between $0.5$0.5 and $1$1. Looking at our picture, this means our event is likely to happen.

 

Practice questions

Question 1

Question 2

Question 3

 

Sample space

Heads	Tails

In probability, the sample space is a list of all the possible outcomes of an experiment.

Outcomes are the results of an experiment. For example, think about flipping a coin. There are two possible outcomes - a head or a tail. So when we list (or write out) the sample space, we would write:

$\left\{\text{heads, tails}\right\}${heads, tails}

Other examples:

• rolling a dice would have a sample space of $\left\{1,2,3,4,5,6\right\}${1,2,3,4,5,6}
• describing the weather could have a sample space of $\left\{\text{sunny, cloudy, rainy}\right\}${sunny, cloudy, rainy} or $\left\{\text{hot, cold}\right\}${hot, cold}
• answers to a survey of favourite seasons could have a sample space of $\left\{\text{summer, autumn, winter, spring}\right\}${summer, autumn, winter, spring}
• A bag of marbles containing $3$3 red marbles, $2$2 blue marbles and $1$1 green marble has a sample space of $\left\{\text{red, red, red, blue, blue, blue, green}\right\}${red, red, red, blue, blue, blue, green}.

(Note: when there are more than $1$1 of the same outcome possible you need to list them all as individual outcomes like the above example.)

Notice how the sample space is listed? Using curly brackets { }.

There are some common items used in probability questions, including cards, dice, coins so it's good to be familiar with their characteristics.

 

Worked examples

EXAMPLE 1

A jar is filled with $4$4 blue marbles and $3$3 red marbles and one is to be chosen at random. List the sample space.

Think: What are all the possible options for what marble will be selected?

Do: {$\text{blue, blue, blue, blue, red, red, red}$blue, blue, blue, blue, red, red, red}

 

example 2

 The spinner below is spun.

List the sample space.

Think: What are all the possible outcomes?

Do: {$\text{yellow, green, red, blue}$yellow, green, red, blue}

 

Practice question

Question 4