Data and probability · Ages 14–15

Certain, impossible and random events worksheet

Part of: Probability

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Data and probability · Ages 14–15

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

1.A bag holds 5 balls numbered 1 to 5, and one is drawn at random. For "the number drawn is greater than k" to be impossible, the least k can be is .
Answer:
2.A bag holds 11 balls numbered 1 to 11, and one is drawn at random. For "the number drawn is greater than k" to be impossible, the least k can be is .
Answer:
3.A bag holds 7 balls numbered 1 to 7, and one is drawn at random. For "the number drawn is greater than k" to be impossible, the least k can be is .
Answer:
4.A bag holds 20 balls numbered 1 to 20, and one is drawn at random. For "the number drawn is greater than k" to be impossible, the least k can be is .
Answer:
5.A bag holds 17 balls numbered 1 to 17, and one is drawn at random. For "the number drawn is greater than k" to be impossible, the least k can be is .
Answer:

6.An ordinary die is rolled once. Which of these is a certain event?
- A. Rolling a number less than 9
- B. Rolling a number less than 4
- C. Rolling a 7
- D. Rolling an odd number
Choose the right answer
Answer:
7.An ordinary die is rolled once. Which of these is an impossible event?
- A. Rolling a number less than 7
- B. Rolling an even number
- C. Rolling a 1
- D. Rolling a 8
Choose the right answer
Answer:
8.For an ordinary die, "rolling a number greater than 0" is a certain event.
True or false?
Answer:
9.A bag holds 6 red balls and 0 green ones, and nothing else. One is drawn at random; "a red ball" is a random event.
True or false?
Answer:
10.A bag holds 3 red balls and 2 green ones, and nothing else. One is drawn at random; "a red ball" is a random event.
True or false?
Answer:
11.A bag holds 1 red balls and 4 green ones, and nothing else. One is drawn at random; "a red ball" is a random event.
True or false?
Answer:
12.Which of these is a random event?
- A. Tossing a coin and getting heads
- B. A year having 14 months
- C. Among 17 people, at least two born in the same month
- D. A stone thrown up into the air coming down
Choose the right answer
Answer:

13.A game's spinner has 8 equal parts numbered 1 to 8, as shown. Spun once, what kind of event is "it stops on a number greater than 8"?
- A. Certain
- B. Random
- C. Impossible
- D. It can't be told
Choose the right answer
Working:
Answer:
14.A drawer holds socks in 2 colours, 8 of each, all mixed up. In the dark, at least how many must be taken to be sure of two the same colour?
Working:
Answer:
15.Ka-yee's box holds 6 red balls and 6 blue, nothing else. One is drawn at random. Four events: a red ball; a yellow ball; a red or blue ball; a blue ball. of them are certain, impossible and random.
Fill in each blank
Working:
Answer:
16.A lucky-draw box holds 27 tickets, 25 of them winners. Ka-lok draws one; "a winning ticket" is a certain event.
True or false?
Working:
Answer:
17.May's bag holds 7 red balls and 7 blue. With eyes shut, May takes them out one by one without putting any back. At least how many must come out for "a red one among them" to be certain?
Working:
Answer:
18.Tsz-hin's bag holds 4 red balls and 8 blue. With eyes shut, Tsz-hin takes them out one by one without putting any back. At least how many must come out for "a red one among them" to be certain?
Working:
Answer:

Show the answers and working

Certain, impossible and random events worksheet: Answers and working

1. 5
The largest number is 5. When k is 5 or more, no number beats it; when k is less than 5, drawing 5 does.
2. 11
The largest number is 11. When k is 11 or more, no number beats it; when k is less than 11, drawing 11 does.
3. 7
The largest number is 7. When k is 7 or more, no number beats it; when k is less than 7, drawing 7 does.
4. 20
The largest number is 20. When k is 20 or more, no number beats it; when k is less than 20, drawing 20 does.
5. 17
The largest number is 17. When k is 17 or more, no number beats it; when k is less than 17, drawing 17 does.

6. A. Rolling a number less than 9
Every one of 1 to 6 is less than 9, so whatever comes up, the event happens.
7. D. Rolling a 8
A die shows only 1 to 6, never 8, so rolling a 8 can't happen.
8. True
A die shows 1 to 6. The event is certain only if all of 1 to 6 are greater than 0, that is, if 0 is less than 1.
9. False
The bag has 0 green balls. With any green ones, a red may or may not come out, so it is random; with none, red is certain.
10. True
The bag has 2 green balls. With any green ones, a red may or may not come out, so it is random; with none, red is certain.
11. True
The bag has 4 green balls. With any green ones, a red may or may not come out, so it is random; with none, red is certain.
12. A. Tossing a coin and getting heads
A coin may land heads or tails; the outcome can't be known beforehand, so it is random.

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

13. C. Impossible
The numbers are 1 to 8; check which beat 8: all of them is certain, none impossible, some random.
14. 3 socks
At worst the first 2 are all different colours; the next, number 3, must match one.
15. 1, 1, 2
"Red or blue" takes in every outcome: certain. There is no yellow ball: impossible. "Red" and "blue" may or may not happen: random.
16. False
25 of the 27 tickets win. Only if all of them win is winning certain; otherwise it is random.
17. 8 balls
At worst all 7 blue come out first; the next one must be red: 7 + 1 = 8.
18. 9 balls
At worst all 8 blue come out first; the next one must be red: 8 + 1 = 9.

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