Data and charts · Ages 8–9
Fair and unfair games worksheet
Part of: Chance and probability
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Fair and unfair games worksheet
Data and charts · Ages 8–9
Numsprite
numsprite.com
Name:Date:Score:／48
Write each answer in the space. For word problems, show your working and write a sentence answer.
Part A: Working out and filling in (2 marks each)
1.Ka-lok and Chi-keung take a ball from this bag: red 🔴 and Ka-lok wins, blue 🔵 and Chi-keung wins. What is the fewest balls to put in to make the game fair?
Answer:
2.Ka-yan and Ming take a ball from this bag: red 🔴 and Ka-yan wins, blue 🔵 and Ming wins. What is the fewest balls to put in to make the game fair?
Answer:
3.Tsz-ching and Ming spin this spinner: red 🔴 and Tsz-ching wins, blue 🔵 and Ming wins. What is the fewest red parts to repaint blue to make the game fair?
Answer:
4.Tsz-hin and Ka-lok spin this spinner: red 🔴 and Tsz-hin wins, blue 🔵 and Ka-lok wins. What is the fewest red parts to repaint blue to make the game fair?
Answer:
Part B: Choose, or true or false (2 marks each)
5.Tsz-ching and Ka-yan roll a dice. Which rule is fair?
- A. More than 5: Tsz-ching wins; anything else: Ka-yan wins
- B. A 3: Tsz-ching wins; anything else: Ka-yan wins
- C. 1 to 1: Tsz-ching wins; anything else: Ka-yan wins
- D. Odd: Tsz-ching wins; even: Ka-yan wins
Choose the right answer
Answer:
6.Tsz-hin and Ming spin this spinner: red 🔴 and Tsz-hin wins; blue 🔵 and Ming wins. The game is fair.
True or false?
Answer:
7.Tsz-hin and Ka-yee spin this spinner: red 🔴 and Tsz-hin wins; blue 🔵 and Ka-yee wins. The game is fair.
True or false?
Answer:
8.Tsz-hin and Tsz-ching roll a dice. Which rule is fair?
- A. More than 5: Tsz-hin wins; anything else: Tsz-ching wins
- B. 1 to 5: Tsz-hin wins; anything else: Tsz-ching wins
- C. Odd: Tsz-hin wins; even: Tsz-ching wins
- D. A 2: Tsz-hin wins; anything else: Tsz-ching wins
Choose the right answer
Answer:
9.Tsz-hin and Ka-yan play with a spinner: red 🔴 and Tsz-hin wins, blue 🔵 and Ka-yan wins. Which spinner makes the game fair?
- A
- B
- C
- D
Choose the right picture
Answer:
10.Chi-keung and May play with a spinner: red 🔴 and Chi-keung wins, blue 🔵 and May wins. Which spinner makes the game fair?
- A
- B
- C
- D
Choose the right picture
Answer:
11.May and Tsz-ching spin this spinner: red 🔴 and May wins, blue 🔵 and Tsz-ching wins, yellow 🟡 and they spin again. What about this game?
- A. It is fair
- B. Unfair: Tsz-ching is likelier to win
- C. Unfair: May is likelier to win
- D. Unfair, because of the yellow
Choose the right answer
Answer:
12.Ming and Tsz-hin spin this spinner: red 🔴 and Ming wins, blue 🔵 and Tsz-hin wins, yellow 🟡 and they spin again. What about this game?
- A. Unfair, because of the yellow
- B. It is fair
- C. Unfair: Ming is likelier to win
- D. Unfair: Tsz-hin is likelier to win
Choose the right answer
Answer:
Part C: Word problems (4 marks each)
13.A bag holds 5 red, 6 blue and 2 yellow balls. Ka-lok, Ming and Chi-keung play: red and Ka-lok wins, blue and Ming wins, yellow and Chi-keung wins. Only adding balls, what is the fewest balls to put in to make the game fair?
Working:
Answer:
14.Ka-yee and Chi-keung play with number cards 1 to 20, taking one without looking: 3 or less and Ka-yee wins; anything else and Chi-keung wins. To make the game fair, what should “3” be changed to?
Working:
Answer:
15.Ka-yee and Ka-yan toss a $1 coin and a $2 coin together. Which rule is fair?
- A. One of each: Ka-yee wins; both heads: Ka-yan wins; both tails: toss again
- B. At least one head: Ka-yee wins; anything else: Ka-yan wins
- C. Both the same: Ka-yee wins; different: Ka-yan wins
- D. Both heads: Ka-yee wins; anything else: Ka-yan wins
Choose the right answer
Working:
Answer:
16.A spinner has 6 equal parts: 2 red and the other 4 blue. Red and May wins; blue and Ka-yan wins. How many blue parts must be changed to red to make the game fair?
Working:
Answer:
17.Ka-lok and Ming toss a $1 coin and a $2 coin together. Which rule is fair?
- A. Both heads: Ka-lok wins; anything else: Ming wins
- B. At least one head: Ka-lok wins; anything else: Ming wins
- C. Both the same: Ka-lok wins; different: Ming wins
- D. One of each: Ka-lok wins; both heads: Ming wins; both tails: toss again
Choose the right answer
Working:
Answer:
18.A spinner has 12 equal parts: 4 red and the other 8 blue. Red and Tsz-hin wins; blue and May wins. How many blue parts must be changed to red to make the game fair?
Working:
Answer:
Show the answers and working
Fair and unfair games worksheet: Answers and working
Part A: Working out and filling in
1. 4
Count the red and blue balls first. Fair needs the same number of each: which colour do you add?
5 red and 1 blue. Fair needs equal numbers: put 4 into the colour with fewer.
2. 3
Count the red and blue balls first. Fair needs the same number of each: which colour do you add?
4 red and 7 blue. Fair needs equal numbers: put 3 into the colour with fewer.
3. 3
Count all the parts first. Fair means half red and half blue: how many red parts are there too many?
8 parts, so fair means 4 red and 4 blue. There are 7 red: repaint 7 − 4 = 3.
4. 2
Count all the parts first. Fair means half red and half blue: how many red parts are there too many?
12 parts, so fair means 6 red and 6 blue. There are 8 red: repaint 8 − 6 = 2.
Part B: Choose, or true or false
5. D. Odd: Tsz-ching wins; even: Ka-yan wins
A dice has 1 to 6. For each rule, count how many outcomes win for each player.
Odd (1, 3, 5) and even (2, 4, 6) are 3 outcomes each, so both have the same chance.
6. True
The parts are the same size: count the red parts and the blue parts.
The parts are equal: 4 red, 4 blue. Only equal numbers give both the same chance.
7. False
The parts are the same size: count the red parts and the blue parts.
The parts are equal: 5 red, 1 blue. Only equal numbers give both the same chance.
8. C. Odd: Tsz-hin wins; even: Tsz-ching wins
A dice has 1 to 6. For each rule, count how many outcomes win for each player.
Odd (1, 3, 5) and even (2, 4, 6) are 3 outcomes each, so both have the same chance.
9. A
For each spinner, count the red and blue parts. They must be equal.
Only the spinner with as many red parts as blue gives both the same chance.
10. A
For each spinner, count the red and blue parts. They must be equal.
Only the spinner with as many red parts as blue gives both the same chance.
11. B. Unfair: Tsz-ching is likelier to win
Yellow just means spin again, so leave it out. Count the red and the blue parts.
Leave yellow out and compare red (1) with blue (3): equal is fair, otherwise the one with more parts is likelier to win.
12. D. Unfair: Tsz-hin is likelier to win
Yellow just means spin again, so leave it out. Count the red and the blue parts.
Leave yellow out and compare red (1) with blue (3): equal is fair, otherwise the one with more parts is likelier to win.
Part C: Word problems
Marking: 2 for the working, 1 for the answer, 1 for the sentence.
13. 5 balls
Fair needs equal numbers, and you can only add balls. Find how many the commonest colour has first.
Fair needs equal numbers, and balls can only be added, so each colour must reach 6: 3 × 6 − 5 − 6 − 2 = 5.
14. 10
Fair means half the cards each. What is half of the 20 cards?
The 20 cards must split in half, 10 each: 1 to 10 for Ka-yee, the other 10 for Chi-keung.
15. C. Both the same: Ka-yee wins; different: Ka-yan wins
List both coins' outcomes: HH, HT, TH, TT. For each rule, count how many each player gets.
The outcomes are HH, HT, TH, TT: 2 the same and 2 different, so it is fair.
16. 1 part
Fair means the same chance for both: red and blue need half each. What is half of 6 parts?
Fair needs as much red as blue, half of the 6 parts each, 3: 3 − 2 = 1 blue parts must turn red.
17. C. Both the same: Ka-lok wins; different: Ming wins
List both coins' outcomes: HH, HT, TH, TT. For each rule, count how many each player gets.
The outcomes are HH, HT, TH, TT: 2 the same and 2 different, so it is fair.
18. 2 parts
Fair means the same chance for both: red and blue need half each. What is half of 12 parts?
Fair needs as much red as blue, half of the 12 parts each, 6: 6 − 4 = 2 blue parts must turn red.
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