# 12.01 The language of probability

Lesson

## 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.

Remember!

These are $5$5 key terms used to describe chance:

• Impossible: definitely will NOT happen.
• Unlikely: more likely NOT to happen than to happen.
• Even chance: equally likely to happen as not to happen.
• Likely: more likely to happen than not to happen.
• Certain: definitely will happen.
Activity

Discuss as a class where you think these events will fit in the range of probabilities. Describe using a word, a fraction and a decimal. Then you can think of your own events and do the same!

• Christmas will be on the $25$25th of December next year.
• It will rain next week.
• Blue is the most popular colour of students in your school.
• You flip a coin and it lands on heads.

#### Practice questions

##### Question 1

What is the chance that next week will have $8$8 days?

1. Impossible

A

Likely

B

Unlikely

C

Certain

D

Even chance

E

Impossible

A

Likely

B

Unlikely

C

Certain

D

Even chance

E

##### Question 2

A game in a classroom uses this spinner.

1. What is the chance of spinning an odd number?

certain

A

even chance

B

impossible

C

likely

D

certain

A

even chance

B

impossible

C

likely

D
2. What is the chance of spinning a $2$2?

likely

A

impossible

B

certain

C

even chance

D

likely

A

impossible

B

certain

C

even chance

D
3. What is the chance of spinning a number less than $8$8?

likely

A

impossible

B

even chance

C

certain

D

likely

A

impossible

B

even chance

C

certain

D

##### Question 3

A probability of $0.9$0.9 means:

1. an event in unlikely to occur.

A

an event is likely to occur.

B

an event is certain to occur.

C

an event in unlikely to occur.

A

an event is likely to occur.

B

an event is certain to occur.

C

## Sample space

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.

Common probability topics
• There are $52$52 cards in a standard deck.
• A standard die has $6$6 faces (because it's a cube)
• A coin has $2$2 faces- heads and tails

#### 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

If I pick a whole number between (and including) $3$3 and $7$7, what are all the possible numbers I may have picked?

List your answers on the same line, with a comma between each of them.

### Outcomes

#### MS11-2

represents information in symbolic, graphical and tabular form

#### MS11-7

develops and carries out simple statistical processes to answer questions posed