Data and probability · Ages 14–15

Probability word problems worksheet

Part of: Probability

In the print window, choose “Save as PDF” to download it. The answers print on the last page.

Data and probability · Ages 14–15

Numsprite
numsprite.com

Name:Date:Score:／48

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

1.20 cards are numbered 1 to 20. Ka-lok draws one at random. The probability of a prime is .
Answer in simplest form
Answer:
2.A whole number from 1 to 42 is chosen at random. The probability of a multiple of 4 or 9 is .
Answer in simplest form
Answer:
3.8 cards are numbered 1 to 8. Ka-yee draws one at random. The probability of a prime is .
Answer in simplest form
Answer:
4.The three digit cards below make a three-digit number, each used once. Made at random, the probability it is greater than 800 is .
Answer in simplest form
Answer:
5.The three digit cards below make a three-digit number, each used once. Made at random, the probability it is even is .
Answer in simplest form
Answer:
6.The three digit cards below make a three-digit number, each used once. Made at random, the probability it is greater than 700 is .
Answer in simplest form
Answer:
7.A whole number from 1 to 32 is chosen at random. There are multiples of 4, of 5 and common multiples, so the probability of a multiple of 4 or 5 is .
Fill in each blank
Answer:
8.A whole number from 1 to 43 is chosen at random. There are multiples of 3, of 8 and common multiples, so the probability of a multiple of 3 or 8 is .
Fill in each blank
Answer:

9.A whole number from 1 to 36 is chosen at random. What is the probability of a multiple of 2 or 7?
- A. 118
- B. 712
- C. 1936
- D. 2336
Choose the right answer
Answer:
10.A whole number from 1 to 53 is chosen at random. What is the probability of a multiple of 3 or 7?
- A. 253
- B. 2253
- C. 2453
- D. 2053
Choose the right answer
Answer:
11.Choosing a whole number from 1 to 19, the probability of a multiple of 3 plus that of a multiple of 8 equals the probability of a multiple of 3 or 8.
True or false?
Answer:
12.Choosing a whole number from 1 to 29, the probability of a multiple of 2 plus that of a multiple of 8 equals the probability of a multiple of 2 or 8.
True or false?
Answer:

13.Two of 6 friends are chosen at random to represent the group. Ka-yan is one of the 6. What is the probability Ka-yan is chosen?
Answer in simplest form
Working:
Answer:
14.Raffle numbers run from 1 to 98. A multiple of 3 wins a small prize; if it is also a multiple of 7, it wins the big prize instead. The probability of the big prize is , and of a small prize .
Fill in each blank
Working:
Answer:
15.A car park has 20 spaces numbered 1 to 20; those numbered with a multiple of 2 or 9 have a charger. A car parks in a space at random. What is the probability it can charge?
Answer in simplest form
Working:
Answer:
16.Ka-yee makes a two-digit number from two of the four digit cards below, the tens first, then the units. Made at random, what is the probability it is even?
Answer in simplest form
Working:
Answer:
17.Ka-yan rolls a die twice: the first roll is the tens digit, the second the units. There are possible two-digit numbers; the probability the number is a multiple of 8 is .
Fill in each blank
Working:
Answer:
18.Two of 7 friends are chosen at random to represent the group. Tsz-ching is one of the 7. What is the probability Tsz-ching is chosen?
Answer in simplest form
Working:
Answer:

Show the answers and working

Probability word problems worksheet: Answers and working

1. 25
There are 8 primes from 1 to 20 (1 isn't one): 820 = 25.
2. 1342
Multiples of 4: 10; of 9: 4; of 36, counted twice: 1. 10 + 4 − 1 = 13, so P = 1342 = 1342.
3. 12
There are 4 primes from 1 to 8 (1 isn't one): 48 = 12.
4. 13
A number with hundreds digit 8 or more beats 800 (the other digits aren't 0); the hundreds digit is any of the three cards, 1 of them at least 8: 13 = 13.
5. 13
Even depends on the last digit alone, equally likely any of the three cards, 1 of them even: 13 = 13. Or list all 6 numbers and count.
6. 13
A number with hundreds digit 7 or more beats 700 (the other digits aren't 0); the hundreds digit is any of the three cards, 1 of them at least 7: 13 = 13.
7. 8, 6, 1, 1332
Include and exclude: (8 + 6 − 1) ÷ 32 = 1332.
8. 14, 5, 1, 1843
Include and exclude: (14 + 5 − 1) ÷ 43 = 1843.

9. B. 712
18 + 5 − 2 of them, over 36.
10. B. 2253
17 + 7 − 2 of them, over 53.
11. True
Their least common multiple is 24. If 24 is more than 19, nothing is counted twice and the two simply add; otherwise the common ones must come off.
12. False
Their least common multiple is 8. If 8 is more than 29, nothing is counted twice and the two simply add; otherwise the common ones must come off.

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

13. 13
There are 6 × 5 ÷ 2 = 15 pairs, 5 of them including Ka-yan: 515 = 13.
14. 249, 27
Big: common multiples of 3 and 7, the multiples of 21, P = 249; small: multiples of 3 less the big ones, P = 27.
15. 1120
Multiples of 2: 10; of 9: 2; of both: 1. 10 + 2 − 1 = 11, P = 1120 = 1120.
16. 14
4 × 3 = 12 numbers in all. The units digit is equally likely any of the four cards, 1 of them even: 14 = 14.
17. 36, 536
In a table, 6 × 6 = 36 numbers from 11 to 66; checking each, 5 are multiples of 8: 536 = 536.
18. 27
There are 7 × 6 ÷ 2 = 21 pairs, 6 of them including Tsz-ching: 621 = 27.

Numsprite · numsprite.com/en/worksheets/probability/probability-word-problems