Sample space diagrams

The Maths Habit

Spin both spinners. You win if they land on the same colour. Is this a good game for you?

No. Only 3 of the 9 ways match.

What fraction of the squares have a ring?

26

49

38

Outcome: One way the two spinners can land. It is one square of the grid.
Sample space diagram: A grid that shows every outcome.
Fair: Each section has the same chance.
Total: Add the scores.

+	1	2	3
1	2	3	4
2	3	4	5

2all the squares3ones you want4

P(total is 4) =ones you wantall the squares

1Fill in the grid.Add the number at the side and the number at the top.
2Count them all.Every square in the grid. This number goes on the bottom.
3Count the ones you want.Ring them in the grid. This number goes on the top.
4Write the fraction.Put the top over the bottom.

Add the scores on two fair spinners. Find P(total is 3).

+	1	2	3
1	2	3	4
2	3	4	5

1Fill in the grid.

2Count them all.

6

3Count the ones you want.

2

4Write the fraction.

P(total is 3) =26

Add the scores on two fair spinners. Find P(total is 5).

+	1	2	3
1	2	3	4
2	3	4	5
3	4	5	6

1Fill in the grid.

2Count them all.

9

3Count the ones you want.

2

4Write the fraction.

P(total is 5) =29

Add the scores on two fair spinners. Find P(total is 3).

+	1	2	3
1	2	3	4
2	3	4	5

1Fill in the grid.

2Count them all.

6

3Count the ones you want.

2

4Write the fraction.

P(total is 3) =26

1Fill in the grid.2Count them all.3Count the ones you want.4Write the fraction.

Add the scores on two fair spinners. Find P(total is 4).

+	1	2	3	4
1	2	3	4	5
2	3	4	5	6

1Fill in the grid.

2Count them all.

8

3Count the ones you want.

2

4Write the fraction.

P(total is 4) =28

Add the scores on two fair spinners. Find P(total is 3).

+	1	2	3
1	2	3	4
2	3	4	5

1Fill in the grid.

2Count them all.

6

3Count the ones you want.

2

4Write the fraction.

P(total is 3) =26

1Fill in the grid.2Count them all.3Count the ones you want.4Write the fraction.

Add the scores on two fair spinners. Find P(total is 4).

+	1	2
1	2	3
2	3	4
3	4	5

1Fill in the grid.

2Count them all.

6

3Count the ones you want.

2

4Write the fraction.

P(total is 4) =26

Add the scores on two fair spinners. Find P(total is 3).

+	1	2	3
1	2	3	4
2	3	4	5

1Fill in the grid.

2Count them all.

6

3Count the ones you want.

2

4Write the fraction.

P(total is 3) =26

1Fill in the grid.2Count them all.3Count the ones you want.4Write the fraction.

Add the scores on two fair spinners. Find P(total is 2).

+	1	2	3
1	2	3	4
2	3	4	5
3	4	5	6

1Fill in the grid.

2Count them all.

9

3Count the ones you want.

1

4Write the fraction.

P(total is 2) =19

1Fill in the grid.2Count them all.3Count the ones you want.4Write the fraction.

1Find P(total is 4).

+	1	2	3
1	2	3	4
2	3	4	5

1Fill in the grid.

2Count them all.

6

3Count the ones you want.

2

4Write the fraction.

P(total is 4) =26

2Find P(total is 6).

+	1	2	3
1	2	3	4
2	3	4	5
3	4	5	6

1Fill in the grid.

2Count them all.

9

3Count the ones you want.

1

4Write the fraction.

P(total is 6) =19

3Find P(total is 3).

+	1	2	3	4
1	2	3	4	5
2	3	4	5	6

1Fill in the grid.

2Count them all.

8

3Count the ones you want.

2

4Write the fraction.

P(total is 3) =28

Add the scores on two fair spinners. Find P(total is 5).

+	1	2	3	4
1	2	3	4	5
2	3	4	5	6
3	4	5	6	7

1Fill in the grid.

2Count them all.

12

3Count the ones you want.

3

4Write the fraction.

P(total is 5) =312

Add the scores on two fair spinners. Find P(total is 4).

+	1	2	3	4
1	2	3	4	5
2	3	4	5	6
3	4	5	6	7
4	5	6	7	8

1Fill in the grid.

2Count them all.

16

3Count the ones you want.

3

4Write the fraction.

P(total is 4) =316

Add the scores on two fair spinners. Find P(total is 5).

+	1	2	3	4
1	2	3	4	5
2	3	4	5	6
3	4	5	6	7

1Fill in the grid.

2Count them all.

12

3Count the ones you want.

3

4Write the fraction.

P(total is 5) =312

1Fill in the grid.2Count them all.3Count the ones you want.4Write the fraction.

Add the scores on two fair spinners. Find P(total is 3).

+	1	2	3	4
1	2	3	4	5
2	3	4	5	6
3	4	5	6	7

1Fill in the grid.

2Count them all.

12

3Count the ones you want.

2

4Write the fraction.

P(total is 3) =212

Add the scores on two fair spinners. Find P(total is 5).

+	1	2	3	4
1	2	3	4	5
2	3	4	5	6
3	4	5	6	7

1Fill in the grid.

2Count them all.

12

3Count the ones you want.

3

4Write the fraction.

P(total is 5) =312

1Fill in the grid.2Count them all.3Count the ones you want.4Write the fraction.

Add the scores on two fair spinners. Find P(total is 7).

+	1	2	3	4
1	2	3	4	5
2	3	4	5	6
3	4	5	6	7
4	5	6	7	8

1Fill in the grid.

2Count them all.

16

3Count the ones you want.

2

4Write the fraction.

P(total is 7) =216

Add the scores on two fair spinners. Find P(total is 5).

+	1	2	3	4
1	2	3	4	5
2	3	4	5	6
3	4	5	6	7

1Fill in the grid.

2Count them all.

12

3Count the ones you want.

3

4Write the fraction.

P(total is 5) =312

1Fill in the grid.2Count them all.3Count the ones you want.4Write the fraction.

Jo adds the scores on two fair spinners. She wins with a total of 6. Find P(Jo wins).

+	1	2	3	4	5
1	2	3	4	5	6
2	3	4	5	6	7
3	4	5	6	7	8

1Fill in the grid.

2Count them all.

15

3Count the ones you want.

3

4Write the fraction.

P(Jo wins) =315

Answer sheet

Add the scores. Is it right?
Thumbs up: right. Thumbs down: wrong.

Spinners 1 to 2 and 1 to 3. P(total is 3) = 26
Right
Spinners 1 to 3 and 1 to 3. P(total is 4) = 35
Wrong: the bottom is 9
Spinners 1 to 2 and 1 to 4. P(total is 5) = 28
Right
Spinners 1 to 3 and 1 to 3. P(total is 6) = 29
Wrong: only 1 square is 6
Spinners 1 to 3 and 1 to 4. P(total is 2) = 112
Right

Two fair spinners are numbered 1 to 3. Take the smaller score from the bigger. Find P(difference is 0).
39
Two fair dice are rolled. Add the scores. Find P(total is 10 or more).
636
Two fair spinners are numbered 1 to 3. Add the scores. Amy wins if the total is even. Ben wins if it is odd. Is the game fair?
No: P(even) = 59

Add the scores. Find the probability.
26
Add the scores. Find the probability.
29
Spinners numbered 1 to 3 and 1 to 4. Add the scores. Find P(total is 6).
212

Exit tickets to print