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Probability Spaces

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Probability Spaces

This slide show will demonstrate how to

draw a probability space and use it to

calculate probabilities.

The example will draw a probability

space for a 6 sided and a 12 sided dice.

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First we need a table

Probability Space

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Now consider the 6 sided dice

Probability Space

6Sided

Dice

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There are 6 possible outcomes

Probability Space

6Sided

Dice

1

2

3

4

5

6

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Now consider the 12 sided dice

Probability Space

12 Sided Dice

6Sided

Dice

1

2

3

4

5

6

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There are 12 possible outcomes

Probability Space

12 Sided Dice

6Sided

Dice

1

2

3

4

5

6

1 2 3 4 5 6 7 8 9 10 11 12

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Add the scores per combination

Probability Space

12 Sided Dice

6Sided

Dice

1

2

3

4

5

6

1 2 3 4 5 6 7 8 9 10 11 12

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1 + 1 = 2

Probability Space

12 Sided Dice

6Sided

Dice

21

2

3

4

5

6

1 2 3 4 5 6 7 8 9 10 11 12

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1 + 2 = 3

Probability Space

12 Sided Dice

6Sided

Dice

2 31

2

3

4

5

6

1 2 3 4 5 6 7 8 9 10 11 12

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1 + 3 = 4

Probability Space

12 Sided Dice

6Sided

Dice

2 3 41

2

3

4

5

6

1 2 3 4 5 6 7 8 9 10 11 12

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And so on

Probability Space

12 Sided Dice

6Sided

Dice

2 3 4 5 6 7 8 9 10 11 12 131

2

3

4

5

6

1 2 3 4 5 6 7 8 9 10 11 12

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until the table is filled.

Probability Space

12 Sided Dice

6Sided

Dice

2 3 4 5 6 7 8 9 10 11 12 13

3 4 5 6 7 8 9 10 11 12 13 14

4 5 6 7 8 9 10 11 12 13 14 15

5 6 7 8 9 10 11 12 13 14 15 16

6 7 8 9 10 11 12 13 14 15 16 17

7 8 9 10 11 12 13 14 15 16 17 18

1

2

3

4

5

6

1 2 3 4 5 6 7 8 9 10 11 12

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What use is this?

Probability Space

12 Sided Dice

6Sided

Dice

2 3 4 5 6 7 8 9 10 11 12 13

3 4 5 6 7 8 9 10 11 12 13 14

4 5 6 7 8 9 10 11 12 13 14 155 6 7 8 9 10 11 12 13 14 15 16

6 7 8 9 10 11 12 13 14 15 16 17

7 8 9 10 11 12 13 14 15 16 17 18

1

2

34

5

6

1 2 3 4 5 6 7 8 9 10 11 12

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There are 72possibleoutcomesshown in thistable.

Only one ofthem results ina total of 2.

What is the probability of rolling the two dice

and getting a total score of 2?

Probability Space12 Sided Dice

6Sided

Dice

2 3 4 5 6 7 8 9 10 11 12 13

3 4 5 6 7 8 9 10 11 12 13 14

4 5 6 7 8 9 10 11 12 13 14 15

5 6 7 8 9 10 11 12 13 14 15 16

6 7 8 9 10 11 12 13 14 15 16 17

7 8 9 10 11 12 13 14 15 16 17 18

1 2 3 4 5 6 7 8 9 10 11 12

1

2

3

4

5

6

Consider the question below.

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Consider the question below.

So theprobability is

72

1

What is the probability of rolling the two dice

and getting a total score of 2?

Probability Space12 Sided Dice

6Sided

Dice

2 3 4 5 6 7 8 9 10 11 12 13

3 4 5 6 7 8 9 10 11 12 13 14

4 5 6 7 8 9 10 11 12 13 14 155 6 7 8 9 10 11 12 13 14 15 16

6 7 8 9 10 11 12 13 14 15 16 17

7 8 9 10 11 12 13 14 15 16 17 18

1 2 3 4 5 6 7 8 9 10 11 12

1

2

34

5

6

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Now consider this question.

72 outcomes6 of them result

in a total of 8

9

1

72

8 =

What is the probability of rolling the two dice

and getting a total score of 8?

Probability Space12 Sided Dice

6Sided

Dice

2 3 4 5 6 7 8 9 10 11 12 13

3 4 5 6 7 8 9 10 11 12 13 14

4 5 6 7 8 9 10 11 12 13 14 155 6 7 8 9 10 11 12 13 14 15 16

6 7 8 9 10 11 12 13 14 15 16 17

7 8 9 10 11 12 13 14 15 16 17 18

1 2 3 4 5 6 7 8 9 10 11 12

1

2

34

5

6

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PowerPointsBy S. Howarth

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