Y9 Booster

Lesson 11

Objectives – what you should be able to do by the end of the

lesson

• Systematically record all the outcomes of an experiment

• Understand that increasing the number of times an experiment is repeated generally leads to better estimates of probability

• Understand the links between experimental and theoretical probabilities

Here are some terms to with probability:

Outcome

Sample space

Equally likely

Mutually exclusive

Relative frequency

Fair

likelihood

Working in groups agree the meaning of the term(s) and think how you could explain the meaning to others.

Outcome – When tossing a coin there are two possible outcomes – heads or tails. When throwing a die there are 6 possible outcomes.

Sample space – A sample space is a table or grid showing all the possible outcomes of an experiment.

Equally likely – If you choose a card from a pack of 52 the events diamond, heart, club or spade are equally likely.

Mutually exclusive – events that cannot both occur in one experiment. e.g. throwing a 3 and a 5 with one roll of a dice.

Relative frequency – the experimental probability of an outcome.

Fair – a fair dice is one that is not weighted towards a particular outcome or outcomes. All the outcomes are equally likely.

Likelihood – The chance of something happening in an experiment. An outcome may be likely, very likely, not likely, impossible or certain.

1 2 3 4 5 6

h

t x x x x x x

x x x x x x

Pairs game M11.1a

A child’s game has two windows.

In each window, one of three different animals – a bird, cat or dog – is equally likely to appear.

When both windows show the same animal, the child shouts ‘snap’ (this counts as a ‘success’).

Pairs game M11.1b

Estimate the probability of getting a ‘snap’, like this.

• Cut out the three animal cards, place them face down and shuffle them.

• Pick a card. This represents the animal that appears in window 1.

• Replace the card, face down. Shuffle the cards again.

• Pick a card. This represents the animal that appears in window 2.

Decide how to record this result. Decide how many times you are going to

repeat this process.Use your results to work out the

probability of getting two animals the same.

How many times did you repeat the experiment?

How many ‘snaps’ did you record?

What is the experimental probability of a ‘snap’?

Which is most likely a ‘snap’ or ‘not a snap’?

What are the possible outcomes in the pairs game?

bb, bc, bd, cb, cc, cd, db, dc, dd,

b c d

b bb bc bd

c cb cc cd

d db dc dd

window 2

win

do

w 1

OR

Using the list of outcomes what is the theoretical probability of winning?

What is the theoretical probability of getting a cat and a dog?

What is the theoretical probability of not getting a bird?

How does your experimental probability compare with the theoretical one? Are they the same? If not, why do they differ?

How can you improve your estimate?

Objectives – how have we done?

• Systematically record all the outcomes of an experiment

• Understand that increasing the number of times an experiment is repeated generally leads to better estimates of probability

• Understand the links between experimental and theoretical probabilities

Thank you for

your attention