Data and charts · Ages 8–9
Certain, possible, impossible worksheet
Part of: Chance and probability
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Certain, possible, impossible 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.A bag holds 4 red, 4 blue and 4 green balls. What is the fewest balls you must take out so that taking a red ball becomes certain?
Answer:
2.A bag holds 5 red, 1 blue and 3 green balls. What is the fewest balls you must take out so that taking a red ball becomes certain?
Answer:
3.A bag holds 3 red, 5 blue and 3 green balls. What is the fewest balls you must take out so that taking a red ball becomes certain?
Answer:
4.A bag holds 4 red, 3 blue and 2 green balls. What is the fewest balls you must take out so that taking a red ball becomes certain?
Answer:
Part B: Choose, or true or false (2 marks each)
5.A ball is taken from the bag without looking. Which of these is impossible?
- A. Taking a red ball 🔴
- B. Taking a blue ball 🔵
- C. Taking a yellow ball 🟡
- D. Taking a green ball 🟢
Choose the right answer
Answer:
6.Spin this spinner. It is impossible for it to land on yellow 🟡.
True or false?
Answer:
7.Roll an ordinary dice (1 to 6). Which of these is certain?
- A. Rolling a 9
- B. Rolling a number less than 9
- C. Rolling a 4
- D. Rolling a number greater than 5
Choose the right answer
Answer:
8.A ball is taken from the bag without looking. What is taking a red ball 🔴?
- A. Certain
- B. Possible
- C. Impossible
- D. You can only tell after many tries
Choose the right answer
Answer:
9.A bag holds 12 number cards, numbered 1 to 12. Taking one without looking, getting a number greater than 11 is impossible.
True or false?
Answer:
10.A bag holds 11 number cards, numbered 1 to 11. Taking one without looking, getting a number greater than 3 is impossible.
True or false?
Answer:
11.A bag holds 9 number cards, numbered 1 to 9. Taking one without looking, getting a number greater than 8 is impossible.
True or false?
Answer:
12.A bag holds 12 number cards, numbered 1 to 12. Taking one without looking, getting a number greater than 5 is impossible.
True or false?
Answer:
Part C: Word problems (4 marks each)
13.Today is Saturday. Which of these is certain?
- A. Tomorrow is Monday
- B. This day next week is Tuesday
- C. It will rain tomorrow
- D. Tomorrow is Sunday
Choose the right answer
Working:
Answer:
14.May's pencil case holds 4 red pens and 7 blue pens. May takes them out one at a time without looking. What is the fewest pens May must take out to be certain of a red one?
Working:
Answer:
15.A box holds 10 chocolates that look alike: 5 are nut and the rest are milk. Ming 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:
16.A lucky-draw box holds 30 tickets: 2 of them win and the rest don't. To make every draw certain to win, what is the fewest losing tickets that must be changed into winning ones?
Working:
Answer:
17.A lucky-draw box holds 11 tickets: 8 of them win and the rest don't. To make every draw certain to win, what is the fewest losing tickets that must be changed into winning ones?
Working:
Answer:
18.Today is Sunday. Which of these is certain?
- A. Tomorrow is Tuesday
- B. Tomorrow is Monday
- C. This day next week is Wednesday
- D. It will rain tomorrow
Choose the right answer
Working:
Answer:
Show the answers and working
Certain, possible, impossible worksheet: Answers and working
Part A: Working out and filling in
1. 8
For red to be certain, which colour may be left in the bag? Which balls must go?
Only red balls may be left: all 4 blue and 4 green must go, 8 in all; the red ones stay.
2. 4
For red to be certain, which colour may be left in the bag? Which balls must go?
Only red balls may be left: all 1 blue and 3 green must go, 4 in all; the red ones stay.
3. 8
For red to be certain, which colour may be left in the bag? Which balls must go?
Only red balls may be left: all 5 blue and 3 green must go, 8 in all; the red ones stay.
4. 5
For red to be certain, which colour may be left in the bag? Which balls must go?
Only red balls may be left: all 3 blue and 2 green must go, 5 in all; the red ones stay.
Part B: Choose, or true or false
5. C. Taking a yellow ball 🟡
Count the balls of each colour in the bag. Is there a colour with none at all?
A colour with no balls in the bag can never be taken: impossible. Every colour in the bag is possible.
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. B. Rolling a number less than 9
A dice only shows 1 to 6. Go through the options: only one that every face fits is certain.
The biggest face is 6, and every face is less than 9, so it happens every time.
8. A. Certain
Count the red and blue balls first. Are they all red, none red, or a mix?
The bag has 1 red and 0 blue: all red means certain, no red means impossible, both means possible.
9. False
The biggest number is 12. Compare 12 with 11: is any card greater than 11?
The biggest number is 12. If 12 is greater than 11, a card greater than 11 can come up; if not, there is none, so it is impossible.
10. False
The biggest number is 11. Compare 11 with 3: is any card greater than 3?
The biggest number is 11. If 11 is greater than 3, a card greater than 3 can come up; if not, there is none, so it is impossible.
11. False
The biggest number is 9. Compare 9 with 8: is any card greater than 8?
The biggest number is 9. If 9 is greater than 8, a card greater than 8 can come up; if not, there is none, so it is impossible.
12. False
The biggest number is 12. Compare 12 with 5: is any card greater than 5?
The biggest number is 12. If 12 is greater than 5, a card greater than 5 can come up; if not, there is none, so it is impossible.
Part C: Word problems
Marking: 2 for the working, 1 for the answer, 1 for the sentence.
13. D. Tomorrow is Sunday
Today is Saturday, and the days always go in order. Which option happens every single time?
The days of the week always go in order: after Saturday comes Sunday.
14. 8 pens
Think of the unluckiest case: every pen taken first is blue. There are 7 blue pens.
At worst, the first 7 are all blue; one more must then be red: 7 + 1 = 8.
15. 5, 5
Work out how many milk ones there are first: 5 of the 10 are nut.
Only nut left makes nut certain; no nut left makes it impossible.
There are 10 − 5 = 5 milk ones: eat them all and only nut is left. Eat all 5 nut ones and none is left.
16. 28 tickets
Certain to win means every ticket in the box wins. How many don't win now?
Certain to win means every ticket wins: 30 − 2 = 28 tickets don't, and all must be changed.
17. 3 tickets
Certain to win means every ticket in the box wins. How many don't win now?
Certain to win means every ticket wins: 11 − 8 = 3 tickets don't, and all must be changed.
18. B. Tomorrow is Monday
Today is Sunday, and the days always go in order. Which option happens every single time?
The days of the week always go in order: after Sunday comes Monday.
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