UK Secondary (7-11)
Events that impact on others
Lesson

## Independent or dependent?

When we look at the chance of something happening, there are ways in which the chance, or probability could be affected by what has already happened.

## Independent events

An independent event means that the chances of that event happening are not changed by what happened before. For example, when we flip a coin, there is always a $\frac{1}{2}$12 chance that it will land on heads. It doesn't matter whether you tossed a head or tail before.

To see how this works, let's work through an example where you have four different coloured lunchboxes and look at the chance of a particular colour being chosen each day.

## Dependent events

A dependent event means that the chance of that event changes depending on what happened before. For example, let's say you have a lucky dip full of all different prizes. If you pull a toy car out, could someone else choose that same prize?

Let's look at your lunchbox colours again and see how the chance of picking a particular colour changes when you don't bring them home at the end of the day.

Remember!
• If the events are affected by what has already happened, they are dependent upon each other.
• If it makes no difference to what can happen, they are independent of each other.

#### Worked examples

##### Question 1

A family has a baby girl.

Will this affect the chances of their next baby being a girl?

1. No

A

Yes

B

No

A

Yes

B

##### Question 2

Valerie owns $9$9 red shirts and $9$9 blue shirts.

She randomly chooses a shirt for the day, and she gets a red shirt.

At the end of the day, she puts it into the washing basket.

1. Will this affect the chances of choosing a red shirt tomorrow?

No

A

Yes

B

No

A

Yes

B
2. Will this affect the chances of choosing a blue shirt tomorrow?

Yes

A

No

B

Yes

A

No

B

##### Question 3

Charlie is going to randomly select a card from a standard deck of cards.

1. Which of the following events would affect the chances of picking a red queen next time?

Randomly selecting a red card from the deck and putting it back

A

Randomly selecting a $4$4 from the deck and putting it back

B

Randomly selecting a spade from the deck and not putting it back

C

Randomly selecting a black card from the deck and not putting it back

D

Randomly selecting a red card from the deck and putting it back

A

Randomly selecting a $4$4 from the deck and putting it back

B

Randomly selecting a spade from the deck and not putting it back

C

Randomly selecting a black card from the deck and not putting it back

D