NZ Level 4
Probabilities as Fractions
Lesson

## How likely is something?

Often we can't be certain of something happening, and we are only able to calculate the chance it might happen. We can think of the chance as having levels, and we may use words such as:

• certain
• extremely likely
• very likely
• possible
• unlikely
• very unlikely, and
• impossible

to describe the probability of something happening.

### Fractions to express probability

If we toss a coin, there are $2$2 possible outcomes. We could toss a head, or we could toss a tail. The chance of a head is $1$1 out of a total of $2$2 possible outcomes, so we would write this as $\frac{1}{2}$12.The chance of tossing a tail is also $\frac{1}{2}$12.  The chance, or probability, of tossing a head or a tail is $\frac{1}{1}$11, or $1$1, since it is certain that we will toss either a head or a tail. The chance of tossing neither a head nor a tail is  $\frac{0}{1}$01or 0, since it is impossible  that neither a head nor tail will appear, assuming we are using a standard coin.

If we roll a die, our fractions change, because a die has $6$6 sides. Let's explore this in Video 1.

### combinations

Sometimes, we might want to work out the probability of more than one thing happening. Instead of working out the probability of rolling a $3$3, for example, we might want to know the probability of rolling an odd number. We use exactly the same method that we use for one particular outcome, but we may find there is more than one way in which we can do this. Finally, we need to express our answer as a fraction in its simplest form, and we do this in Video 2. We also investigate a situation that is certain to happen!

Remember!

If it is impossible for something to happen, then the probability will be $0$0. If something will definitely happen, it has a probability of $1$1.

#### Worked Examples

##### Question 1

There are $100$100 cards, numbered $1$1 to $100$100, face down on a table.

1. What is the probability that Lucy picks a card with a number less than $61$61?

##### Question 2

This spinner is spun.

1. What is the probability that it lands on purple?

2. What is the probability that it lands on blue?

3. What is the probability that it lands on yellow?

##### Question 3

Xanthe takes a marble out of the jar without looking.

1. What are all the possible colours Xanthe could choose? Select all the correct answers.

Blue

A

Red

B

Green

C

Yellow

D

Blue

A

Red

B

Green

C

Yellow

D
2. Write a fraction that represents the probability of choosing a red marble.

3. Write a fraction that represents the probability of choosing a blue marble.

4. What is the probability of choosing a yellow marble.

5. Write a simplified fraction that represents the probability of choosing a green marble.

### Outcomes

#### S4-4

Use simple fractions and percentages to describe probabilities