Data and probability · Ages 14–15

Listing outcomes in a table worksheet

Part of: Probability

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Data and probability · Ages 14–15

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

1.Two dice are rolled. The table lists the product of the two. The probability of a product greater than 27 is .
Answer in simplest form
Answer:
2.Ming rolls two dice. The table lists the sum of the two. The probability of a sum of 11 is .
Answer in simplest form
Answer:
3.Two dice are rolled. The table lists the product of the two. The probability of a product greater than 20 is .
Answer in simplest form
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4.Chi-keung rolls two dice. The table lists the sum of the two. The probability of a sum of 3 is .
Answer in simplest form
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5.Chi-keung rolls two dice, and the table lists the difference (larger minus smaller). The sample space has outcomes; of them have a difference of 1.
Fill in each blank
Answer:
6.Spinner A has 4 equal parts numbered 1 to 4; spinner B has 5 numbered 1 to 5. Each is spun once, and the table lists the sum. The probability of a sum greater than 6 is .
Answer in simplest form
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7.Ming tosses a coin and rolls a die together. The probability of tails with a number greater than 0 is .
Answer in simplest form
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8.Ming rolls two dice, and the table lists the difference (larger minus smaller). The sample space has outcomes; of them have a difference of 1.
Fill in each blank
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9.Ka-lok tosses a coin and rolls a die together. The probability of tails with a number greater than 4 is .
Answer in simplest form
Answer:

10.Two dice are rolled. Which sum is the most likely?
- A. 12
- B. 7
- C. 5
- D. 11
Choose the right answer
Answer:
11.Rolling two dice, a sum of 11 is exactly as likely as a sum of 5.
True or false?
Answer:
12.Rolling two dice, a sum of 8 is exactly as likely as a sum of 5.
True or false?
Answer:

13.A fair has two spinners: A with 2 equal parts numbered 1 to 2, B with 4 numbered 1 to 4. Each is spun once, and an even product wins. What is the probability of winning?
Answer in simplest form
Working:
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14.May plays a board game and must roll a total of 3 on two dice to take off. Two dice have possible outcomes, of them totalling 3, so the probability of taking off is .
Fill in each blank
Working:
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15.Tsz-hin tosses a coin and rolls a die together. Listing the sample space gives outcomes; the probability of heads with a number greater than 5 is .
Fill in each blank
Working:
Answer:
16.In a board game, Ka-yee rolls two dice and moves an extra step if at least one shows a 6. What is the probability of the extra step?
Answer in simplest form
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17.Ka-lok plays a game with a friend: two dice are rolled, and if their product is a multiple of 6, Ka-lok wins. What is the probability Ka-lok wins?
Answer in simplest form
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18.A fair has two spinners: A with 8 equal parts numbered 1 to 8, B with 8 numbered 1 to 8. Each is spun once, and an even product wins. What is the probability of winning?
Answer in simplest form
Working:
Answer:

Show the answers and working

Listing outcomes in a table worksheet: Answers and working

1. 112
Of the 36 cells, 3 show more than 27: 336 = 112.
2. 118
The 36 cells are equally likely, and 2 show 11: 236 = 118.
3. 16
Of the 36 cells, 6 show more than 20: 636 = 16.
4. 118
The 36 cells are equally likely, and 2 show 3: 236 = 118.
5. 36, 10
6 × 6 = 36 cells; 10 of them show a difference of 1.
6. 310
The table has 4 × 5 = 20 cells, 6 of them above 6: 620 = 310.
7. 12
In a table, 2 coin outcomes × 6 die outcomes = 12 cells; tails with more than 0 fills 6 of them: 612 = 12.
8. 36, 10
6 × 6 = 36 cells; 10 of them show a difference of 1.
9. 16
In a table, 2 coin outcomes × 6 die outcomes = 12 cells; tails with more than 4 fills 2 of them: 212 = 16.

10. B. 7
A sum of 7 comes from (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1): 6 cells, the table's longest diagonal.
11. False
A sum of 11 fills 2 cells and 5 fills 4. Two sums match only when they add to 14.
12. False
A sum of 8 fills 5 cells and 5 fills 4. Two sums match only when they add to 14.

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

13. 34
The table has 2 × 4 = 8 cells. An odd product needs both odd: 2 cells; even: 8 − 2 = 6, so 68 = 34.
14. 36, 2, 118
In a table, 6 × 6 = 36 cells, 2 totalling 3: 236 = 118.
15. 12, 112
2 × 6 = 12 cells; heads with more than 5: 1 cells, 112 = 112.
16. 1136
The opposite is neither showing 6: 5 × 5 = 25 cells, so P = 1 − 2536 = 1136; or count the row and column with a 6: 6 + 6 − 1 = 11 cells.
17. 512
In a table of products, 15 of the 36 cells are multiples of 6: 1536 = 512.
18. 34
The table has 8 × 8 = 64 cells. An odd product needs both odd: 16 cells; even: 64 − 16 = 48, so 4864 = 34.

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