NZ Level 3
Outcomes of Chance Experiments
Lesson

## What is chance?

When we need to work out the chance of something happening, we won't know for sure if it will actually happen, so we are thinking of the likelihood of it happening. That is what we mean by the chance of something happening. We can also call this the probability of something happening. In order to work out the chance of something happening, we can work through a few steps.

### the options

If we have a red ball, a blue ball, a green ball, and a black ball in a bucket, we can work out what colours might be drawn out of the bucket. Suppose we take one ball out at at time, what are the options we could choose?

Well, we could choose either of these options - blue, green, red, black. What is the chance of drawing out the a blue ball? What is the chance of drawing out a ball that is not blue? Let's work through an example like this in Video 1. You'll also see how we can express our answer in its simplest form, thinking of the factors of a number.

### possible outcomes

Sometimes you might need to work out the chance of something happening from a smaller collection than what you started with. If I had some animal stickers to hand out, and they were made up of four different colours, and four types of animals, you might want to work out the chance of choosing a particular animal, after you've already chosen a colour. The number of possible outcomes would be the number of the colour already chosen, not the total animal stickers.

Video 2 shows you an example of this, and how you can solve it.

### Different size groups

If you have different groups, you still use the same approach to calculate the possibility, or probability of choosing something. Imagine our animal stickers were on place-mats, and not all place-mats had the same number of animals on them. You might choose from one place-mat, and then think about the probability of choosing a particular animal. Let's work through an example like this in Video 3.

Remember!

When we work out the chance, or probability of something happening, we express our answer as a fraction of the total possible outcomes.

#### Worked Examples

##### Question 1

A word game uses the spinner shown in the picture below.

1. List all the possible letters that can be spun.

Write your answers on the same line, and separate your answers with commas.

2. How many possible outcomes are there when the spinner is spun?

3. What is the probability of spinning the letter $H$H?

4. What is the probability of spinning the letter $S$S?

##### Question 2

Use the figures in the picture to answer these questions.

1. Sarah randomly chooses a yellow shape.

How many possible outcomes are there?

2. Sarah randomly chooses one of the yellow shapes.

What is the probability that the yellow shape she picks is a square?

3. Sarah randomly chooses one of the squares.

How many possible outcomes are there?

4. Sarah randomly chooses one of the squares.

What is the probability that the square she picks is grey?

##### Question 3

A class are sitting at their desks in the order shown in the picture.

 Maximilian Tricia Uther James Amy Peter Laura Sarah Ben Neville Tara Tina Fiona Valerie Xavier Roxanne
1. Mr. Crisp decides to choose a student at random from the fourth column of the classroom.

How many possible outcomes are there?

2. A student is chosen at random from the fourth column.

What is the probability that Uther is picked?

3. Mr. Crisp decides to randomly choose which row will be the first to leave for recess.

How many possible outcomes are there?

4. A row is chosen at random.

What is the probability that Ben's row is chosen to leave for recess first?

### Outcomes

#### S3-3

Investigate simple situations that involve elements of chance by comparing experimental results with expectations from models of all the outcomes, acknowledging that samples vary.