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understanding and using the vocabulary of probability and the probability scale

listing all outcomes for single events, and for successive events, in a systematic way and derive related probabilities.

Autumn 2009 exclusive customer content

This presentation has been developed for use with the new GCSE exam specifications for 2010 and covers:

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Probability

An event can have several outcomes. Each outcome of a given event has a probability or a chance of occurring.

Imagine you roll two six-sided dice. What is the likelihood of:

the combined score being an even number?

the combined score being more than 12?

the combined score being a whole number?

2impossible certaineven chance

0 11

Use the probability scale below to help you make your choice.

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Horse play

The following slide contains an experiment for you to conduct.

The experiment has 12 horses, numbered 1 – 12, and two six-sided dice.

Throw the dice and total up the combined score.

The horse whose number matches the combined score of the dice will move forward one space.

The first horse to the finish line is the winner.

Which horse do you think will win? Why?Conduct the experiment to find out if you are right.

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Horse race game

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Which horses are unlikely to win and why?

Are there any horses that can’t win?

Which horse has the best chance of winning?

How would the game change if you used ten-sided dice?

What combinations of scores give a total of 8?

How many combinations produce a total of 12?

Horse race game

Using the knowledge you have picked up from the experiment, can you answer the following questions?

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36 18

36 12

7

8

9

10

11

ProbabilityWaysCombinationsHorse

3

4

12

6

5

2

1

61,6 6,1 2,5 5,2 3,4 4,3

52,6 6,2 3,5 5,3 4,4

43,6 3,6 4,5 5,4

34,6 4,6 5,5

25,6 6,5

21,2 2,1

31,3 3,1 2,2

16,6

51,5 5,1 2,4 4,2 3,3

41,4 4,1 2,3 3,2

11,1

00136

536

536

136

236

= 118

2 = 1

336 =

112

3 = 1

436 =

19

436 = 1

9

636 = 1

6

Combinations on two dice

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96

5

4

83

2

31

654321+

Second dice

Fir

st d

ice

Sample space diagrams

Another way of displaying all the outcomes from throwing two dice is a sample space diagram.

Colour in all the twos one colour, the threes another colour and so on.

Fill in the rest of the cells in the table.

What patterns do you notice in the table?

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1) What is the probability of getting a total more than 5?

2) What is the probability of getting a total less than 10?

3) What is the probability of getting a total that is a square number?

4) What is the probability of getting an even total?

5) What is the probability of getting an odd total?

6) What is the probability of getting a total less than 13?

1211109876

111098765

10987654

9876543

8765432

7654321

654321+

Second dice

Fir

st d

ice

121110987

11109876

1098765

987654

876543

765432

Sample space diagrams

Now make up your own questions!

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Horse game with 8-sided dice