Data and charts · Ages 8–9

Listing all the outcomes worksheet

Part of: Chance and probability

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Data and charts · Ages 8–9

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Write each answer in the space. For word problems, show your working and write a sentence answer.

1.A spinner has 7 equal parts numbered 1 to 7. It is spun once. How many different outcomes are there?
Answer:
2.A ball is taken from the bag without looking. How many different colours could it be?
Answer:
3.A spinner has 9 equal parts numbered 1 to 9. It is spun once. How many different outcomes are there?
Answer:
4.Toss a coin, then spin this spinner: “heads, red” is one outcome. How many outcomes are there in all?
Answer:
5.Make two-digit numbers with the cards 6, 2 and 0, using two cards each time. How many different two-digit numbers can be made?
Answer:
6.Spinner A shows 1 to 2 and spinner B shows 1 to 4. Spin each once and add the two numbers. There are outcomes in all, and of them give a total of 4.
Fill in each blank
Answer:
7.Spinner A shows 1 to 3 and spinner B shows 1 to 3. Spin each once and add the two numbers. There are outcomes in all, and of them give a total of 4.
Fill in each blank
Answer:
8.Make two-digit numbers with the cards 9, 1 and 4, using two cards each time. How many different two-digit numbers can be made?
Answer:

9.Take one of the number cards 5 and 9 without looking, then toss a coin (H heads, T tails). Which list shows all the outcomes?
- A. 5, 9, H, T
- B. 5H, 9T
- C. 5H, 5T, 9H
- D. 5H, 5T, 9H, 9T
Choose the right answer
Answer:
10.Roll a dice once. “Rolling a 2” and “rolling a number greater than 4” can happen at the same time.
True or false?
Answer:
11.Take one of the number cards 6 and 9 without looking, then toss a coin (H heads, T tails). Which list shows all the outcomes?
- A. 6, 9, H, T
- B. 6H, 6T, 9H, 9T
- C. 6H, 6T, 9H
- D. 6H, 9T
Choose the right answer
Answer:
12.Roll a dice once. “Rolling a 3” and “rolling a number greater than 2” can happen at the same time.
True or false?
Answer:

13.Ka-yan rolls a red dice and a blue dice and adds the scores. How many outcomes give a total of 10?
Working:
Answer:
14.May has three digit cards: 8, 4 and 0. Each time May takes two of them to make a two-digit number. How many different two-digit numbers can May make?
Working:
Answer:
15.Ka-yan plays a lucky-draw game: toss a coin, then take one of the number cards 1 to 7. There are outcomes in all, and of them are heads with an odd number.
Fill in each blank
Working:
Answer:
16.A cha chaan teng breakfast lets you choose one of 4 main dishes and one of 5 drinks. How many different combinations are there?
Working:
Answer:
17.Tsz-ching has three digit cards: 5, 3 and 2. Each time Tsz-ching takes two of them to make a two-digit number. How many different two-digit numbers can Tsz-ching make?
Working:
Answer:
18.Ming rolls a red dice and a blue dice and adds the scores. How many outcomes give a total of 11?
Working:
Answer:

Show the answers and working

Listing all the outcomes worksheet: Answers and working

1. 7 outcomes
Each part gives a different number. Count the parts.
Every part has a different number, so each part is one outcome: 7 in all.
2. 5
The outcomes are colours, not balls: count how many different colours are in the bag.
The outcomes are colours, not balls: the bag holds 5 different colours.
3. 9 outcomes
Each part gives a different number. Count the parts.
Every part has a different number, so each part is one outcome: 9 in all.
4. 4
Count the spinner's colours first, then think how many each of heads and tails can go with.
The spinner has 2 colours. Heads with each colour gives 2, tails with each gives 2 more: 2 + 2 = 4.
5. 4
Fix the tens digit, then pair it with each ones digit in turn. Remember 0 can't be the tens digit.
Fix the tens digit, then pair it with each ones digit in turn; 0 can't be the tens digit. 4 in all.
6. 8, 2
Draw a table: A's 1 to 2 down the side, B's 1 to 4 along the top, and write each total in its box.
Draw a table, A's 2 numbers down the side and B's 4 along the top: 8 boxes, and 2 of them total 4.
7. 9, 3
Draw a table: A's 1 to 3 down the side, B's 1 to 3 along the top, and write each total in its box.
Draw a table, A's 3 numbers down the side and B's 3 along the top: 9 boxes, and 3 of them total 4.
8. 6
Fix the tens digit, then pair it with each ones digit in turn. Remember 0 can't be the tens digit.
Fix the tens digit, then pair it with each ones digit in turn; 0 can't be the tens digit. 6 in all.

9. D. 5H, 5T, 9H, 9T
Fix card 5 with heads and tails, then card 9 with heads and tails. Check each list against that.
Fix the card first: 5 with H and T, then 9 with H and T: 4 in all.
10. False
There is only one roll, and it shows 2. Is 2 greater than 4?
With one roll, both happen only if the 2 rolled is greater than 4.
11. B. 6H, 6T, 9H, 9T
Fix card 6 with heads and tails, then card 9 with heads and tails. Check each list against that.
Fix the card first: 6 with H and T, then 9 with H and T: 4 in all.
12. True
There is only one roll, and it shows 3. Is 3 greater than 2?
With one roll, both happen only if the 3 rolled is greater than 2.

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

13. 3 outcomes
Draw a table, red scores down the side and blue along the top, and find the boxes that total 10.
In a table of red 1–6 against blue 1–6, count the boxes totalling 10 (red 1 blue 2 differs from red 2 blue 1): 3.
14. 4 numbers
Fix 8 in the tens and list the cards that can go in the ones; then put another card in the tens. Careful: can the tens digit be 0?
List them in order: each card takes a turn in the tens (0 can't), and either of the other two goes in the ones. 2 choices for the tens, 2 each: 4 in all.
15. 14, 4
Heads goes with each of the 7 cards, and so does tails. Then list the odd numbers from 1 to 7.
Heads with the 7 cards and tails with the 7 cards: 14 in all. Heads with an odd card: there are 4 odd numbers from 1 to 7.
16. 20 combinations
Fix one main dish first: how many drinks can it go with? Every dish is the same.
Each main dish goes with each of the 5 drinks; list them dish by dish: 4 dishes give 20.
17. 6 numbers
Fix 5 in the tens and list the cards that can go in the ones; then put another card in the tens. Careful: can the tens digit be 0?
List them in order: each card takes a turn in the tens (0 can't), and either of the other two goes in the ones. 3 choices for the tens, 2 each: 6 in all.
18. 2 outcomes
Draw a table, red scores down the side and blue along the top, and find the boxes that total 11.
In a table of red 1–6 against blue 1–6, count the boxes totalling 11 (red 1 blue 2 differs from red 2 blue 1): 2.

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