Probability
UK Secondary (7-11)
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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

 

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