# Events that can/can't happen with others

Lesson

## Is it possible?

When we think of things happening, we know some things can't occur at the same time. You can't be sleeping at the same time as you are awake. If you are standing up, you are not sitting down.

Then there are things that may happen at the same time. You might be standing up, or you might be eating. It's also possible that you are standing up and eating!

From the three arrows below, is it possible to choose an arrow that is straight and green?

While we can choose a green arrow and we can choose a straight arrow, we cannot choose one that satisfies both options. The only straight arrow is red. The only green arrow is curved. Therefore, none of the options satisfies both conditions we were looking for.

## Only two outcomes

Sometimes there are only two possibilities that could occur. If you think of tossing a coin, we can only toss a head or a tail. If we only have one coin, there are no other options that could occur at the same time.

In our first video, we will look at events where there can only be two possibilities.

## More than two outcomes

Sometimes, such as when you throw a die, you have more things that could happen. A die has $6$6 sides. If we only have one die, then we can only roll a $1,2,3,4,5$1,2,3,4,5 or $6$6. We can't roll a $12$12, as we only have one die.

A deck of cards has $52$52 cards. Within a deck of cards, there are different colours, numbers and patterns. This means there are many possibilities of things that could happen. In the second video, we look at having different options, to see what is possible.

#### Worked Examples

##### QUESTION 1

Is it possible for the following two events to happen at the same time?

1) It is a Friday

2) It is raining

1. No

A

Yes

B

No

A

Yes

B

##### QUESTION 2

A die is rolled.

Is it possible for the following two outcomes to happen at the same time?

1) Rolling a $6$6

2) Rolling an odd number

1. No

A

Yes

B

No

A

Yes

B

##### QUESTION 3

A dog is randomly selected from the group of dogs shown.

Which of the following outcomes could happen at the same time?

1. Selecting a dog that is running

A

Selecting a dog with something in its mouth

B

Selecting a dog with spots

C

Selecting a dog with its tongue out

D

Selecting a dog that is running

A

Selecting a dog with something in its mouth

B

Selecting a dog with spots

C

Selecting a dog with its tongue out

D

### 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.