Data and charts · Ages 8–9
Chance and probability worksheet
Covers: Certain, possible, impossible, Probability: more or less likely, Listing all the outcomes, Probability as a fraction, Experiments and their results, Fair and unfair games
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Chance and probability 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.Make two-digit numbers with the cards 5, 4 and 0, using two cards each time. How many different two-digit numbers can be made?
Answer:
2.A ball is taken from the bag without looking. What is the chance of red 🔴, as a fraction?
Answer in simplest form
Answer:
3.Tsz-hin tossed a coin and recorded the results in the table. How many times did Tsz-hin toss it?
Answer:
4.This spinner's parts are all the same size and all different colours. Tsz-ching spins it 14 times. About how many times should each colour come up?
Answer:
5.Ka-yee and Ka-yan take a ball from this bag: red 🔴 and Ka-yee wins, blue 🔵 and Ka-yan wins. What is the fewest balls to put in to make the game fair?
Answer:
Part B: Choose, or true or false (2 marks each)
6.Spin this spinner. It is impossible for it to land on yellow 🟡.
True or false?
Answer:
7.A ball is taken from the bag without looking. What is taking a red ball 🔴?
- A. Possible
- B. You can only tell after many tries
- C. Impossible
- D. Certain
Choose the right answer
Answer:
8.A ball is taken without looking from bag A or bag B. Which bag gives a better chance of red 🔴?
- A. Bag A
- B. You can only tell by trying
- C. Bag B
- D. The chances are the same
Choose the right answer
Answer:
9.Each bag holds 8 balls. From which bag is a ball taken without looking most likely to be red 🔴?
- A
- B
- C
- D
Choose the right picture
Answer:
10.Roll a dice once. “Rolling a 1” and “rolling a number greater than 3” can happen at the same time.
True or false?
Answer:
11.Which spinner gives a 13 chance of landing on red 🔴?
- A
- B
- C
- D
Choose the right picture
Answer:
12.Tsz-ching and May spin this spinner: red 🔴 and Tsz-ching wins, blue 🔵 and May wins, yellow 🟡 and they spin again. What about this game?
- A. Unfair, because of the yellow
- B. Unfair: May is likelier to win
- C. Unfair: Tsz-ching is likelier to win
- D. It is fair
Choose the right answer
Answer:
Part C: Word problems (4 marks each)
13.A box holds 11 chocolates that look alike: 3 are nut and the rest are milk. Ka-lok takes one without looking. If milk ones were eaten first, the next would be certain to be nut; if nut ones were eaten first, a nut one would be impossible.
Fill in each blank
Working:
Answer:
14.Ka-yan may choose bag A or bag B and take one ball without looking; a red ball wins. Bag A holds 3 red and 7 blue; bag B holds 6 red and 4 blue. Which bag should Ka-yan choose?
- A. It makes no difference
- B. Bag B
- C. Neither can win
- D. Bag A
Choose the right answer
Working:
Answer:
15.A cha chaan teng breakfast lets you choose one of 3 main dishes and one of 3 drinks. How many different combinations are there?
Working:
Answer:
16.A box of mooncakes holds 4 lotus seed, 1 red bean and 5 mixed nut ones, all wrapped alike. Tsz-hin takes one without looking. What is the chance of red bean, as a fraction?
Answer in simplest form
Working:
Answer:
17.Tsz-ching tosses a coin 35 times and finds 9 more heads than tails. How many heads were there?
Working:
Answer:
18.A spinner has 12 equal parts: 2 red and the other 10 blue. Red and Ka-yee 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
Chance and probability worksheet: Answers and working
Part A: Working out and filling in
1. 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.
2. 512
Count the red balls, then all the balls in the bag. Chance = wanted ÷ all.
5 red out of 12 balls: chance = 512.
3. 38
Every toss gives one result. Read off how many heads and how many tails are in the table.
Every toss gives one result: 20 heads and 18 tails make 38.
4. 7
Count the spinner's colours. They are equally likely, so the 14 spins are shared equally among them.
The 2 colours are equally likely, so share 14 spins among them: 14 ÷ 2 = 7.
5. 1
Count the red and blue balls first. Fair needs the same number of each: which colour do you add?
6 red and 7 blue. Fair needs equal numbers: put 1 into the colour with fewer.
Part B: Choose, or true or false
6. True
Look at the spinner part by part. Is any part yellow?
Look at the spinner: if any part is yellow, landing on yellow is possible; only with no yellow at all is it impossible.
7. A. Possible
Count the red and blue balls first. Are they all red, none red, or a mix?
The bag has 4 red and 5 blue: all red means certain, no red means impossible, both means possible.
8. A. Bag A
Count the red and blue in both bags. With the same red, see which bag has fewer blue.
Both bags have 4 red; the bag with fewer blue balls has red as a bigger share: A has 1 blue, B has 2.
9. B
Every bag holds 8 balls, so just count the red in each bag and compare.
Every bag holds the same number, so the bag with the most red (7) gives the best chance.
10. False
There is only one roll, and it shows 1. Is 1 greater than 3?
With one roll, both happen only if the 1 rolled is greater than 3.
11. B
For each spinner, count: how many parts altogether, and how many red?
Only a spinner with 3 parts, 1 of them red, gives 13.
12. C. 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 (4) 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. 8, 3
Work out how many milk ones there are first: 3 of the 11 are nut.
Only nut left makes nut certain; no nut left makes it impossible.
There are 11 − 3 = 8 milk ones: eat them all and only nut is left. Eat all 3 nut ones and none is left.
14. B. Bag B
Do the two bags hold the same number of balls? Find each bag's total first, then compare the red.
Both bags hold 10 balls, so the one with more red is better: compare 3 and 6.
15. 9 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 3 drinks; list them dish by dish: 3 dishes give 9.
16. 110
Work out how many mooncakes there are altogether, then see that 1 are red bean.
4 + 1 + 5 = 10 mooncakes, 1 of them red bean: 110.
17. 22 times
Heads and tails make 35, with 9 more heads. Set the extra 9 aside first.
Heads and tails make 35, with 9 more heads: (35 + 9) ÷ 2 = 22 (13 tails).
18. 4 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 − 2 = 4 blue parts must turn red.
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