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Simple probability and independent events

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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

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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

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A coin and a ten-sided dice are thrown and the outcomes recorded in the two-way table below.

1 2 3 4 5 6 7 8 9 10

H 1,H 2,H 3,H 4,H 5,H 6,H 7,H 8,H 9,H 10,H

T 1,T 2,T 3,T 4,T 5,T 6,T 7,T 8,T 9,T 10,T

Dice

Co

inSample space diagrams

1) How many outcomes are there?

2) What is the probability of heads and an even number?

3) What is the probability of tails and a square number?

Make up a fair game and an unfair game based on scoring points from outcomes in the table.