Probability · Ages 14–15
Probability word problems
Multiples of 3 or 5: 10 + 6 − 2; take off the ones counted twice.
How to do it
Method
Multiples of 3 or 5: 10 + 6 − 2; take off the ones counted twice
1 to 30: (10 + 6 − 2) ÷ 30 = 715
Another way
Listing them
3, 5, 6, 9, 10, 12, 15, 18, 20, 21, 24, 25, 27, 30: 14
In full
In a word problem, find two things first: how many outcomes are possible, and how many are favourable. For divisibility, "a multiple of 3 or 5" from 1 to 30: one way is to include and exclude. Multiples of 3: 30 ÷ 3 = 10; of 5: 30 ÷ 5 = 6; both (multiples of 15): 30 ÷ 15 = 2, counted twice, so 10 + 6 − 2 = 14, and P = 1430 = 715. Another way is to list them: 3, 5, 6, 9, 10, 12, 15, 18, 20, 21, 24, 25, 27, 30, also 14. Making numbers from digit cards, count all the numbers that can be made, then the ones that fit: cards 1, 2, 3 make 3 × 2 × 1 = 6 three-digit numbers; an even one ends in 2, and there are 2 × 1 = 2 of them, so P = 26 = 13. Or look at the last digit alone: it is one of the three cards, equally likely, so it is 2 with probability 13.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
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
Show the answer and working
Answer: 23
Even depends on the last digit alone, equally likely any of the three cards, 2 of them even: 23 = 23. Or list all 6 numbers and count.
Example 2
A whole number from 1 to 52 is chosen at random. There are multiples of 4, of 9 and common multiples, so the probability of a multiple of 4 or 9 is .
Fill in each blank
Show the answer and working
Answer: 13, 5, 1, 1752
Include and exclude: (13 + 5 − 1) ÷ 52 = 1752.
Example 3
Choosing a whole number from 1 to 12, the probability of a multiple of 4 plus that of a multiple of 9 equals the probability of a multiple of 4 or 9.
True or false?
Show the answer and working
Answer: True
Their least common multiple is 36. If 36 is more than 12, nothing is counted twice and the two simply add; otherwise the common ones must come off.
Practice questions to try
Try these 5; the answers are at the end. For a whole worksheet, see VIP worksheets below.
1.12 cards are numbered 1 to 12. Ka-yan draws one at random. The probability of a prime is .
Answer in simplest form
Answer:
2.A whole number from 1 to 36 is chosen at random. The probability of a multiple of 2 or 3 is .
Answer in simplest form
Answer:
3.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:
4.A whole number from 1 to 59 is chosen at random. What is the probability of a multiple of 2 or 5?
- A. 3059
- B. 3559
- C. 559
- D. 4059
Choose the right answer
Answer:
5.A whole number from 1 to 39 is chosen at random. There are multiples of 2, of 9 and common multiples, so the probability of a multiple of 2 or 9 is .
Fill in each blank
Answer:
All the answers
- 1. 512
- 2. 23
- 3. 23
- 4. B. 3559
- 5. 19, 4, 2, 713
VIP practice notes and papers
Aimed at tests and exams: questions on this topic, new every time, to print or save as a PDF.
- Practice notes: The key point, worked examples step by step, then questions of the same kind to follow, hints fading
- Practice paper: Set out in parts like a school paper, marked, with answers and full working
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