A whole number from 1 to 20 is chosen at random. The probability of a multiple of 4 is □. Answer in simplest form

1/4. 20 ÷ 4 has whole part 5, so there are 5 multiples of 4: 5/20 = 1/4.

A box holds 3 red balls and 7 blue ones. One is drawn at random. What is the probability of red? A. 3/7 B. 7/10 C. 1/10 D. 3/10 Choose the right answer

D. 3/10. There are 10 balls, 3 of them red: P(red) = 3/10.

Probability · Ages 14–15

Equally likely outcomes

P = favourable ÷ all outcomes, in simplest form.

How to do it

Method

P = favourable ÷ all outcomes, in simplest form

3 red, 5 blue: P(red) = 3 ÷ 8 = 38

Another way

One take away

1 − 520 = 34

In full

When every outcome is equally likely (a fair die, a ball or card drawn at random, a spinner of equal parts), P(event) = the number of favourable outcomes ÷ the number of possible outcomes. A bag of 3 red and 5 blue balls gives a red with probability 3 ÷ (3 + 5) = 38: the bottom is all the balls, not the blue ones (35 is the ratio of red to blue, not a probability). Give the answer in its simplest form. Another way: find the probability it doesn't happen and take it from 1. Choosing from 1 to 20, "not a multiple of 4": there are 20 ÷ 4 = 5 multiples, so P = 1 − 520 = 34; counting straight, 20 − 5 = 15 numbers, 1520 = 34, the same. To count multiples, divide and drop the remainder: from 1 to 30 there are 30 ÷ 4 = 7 r 2, so 7 multiples of 4.

Worked examples

Have a go first, then open each one for the answer and the working.

Example 1
A bag holds 3 red balls (R), 1 blue (B) and 2 yellow (Y), as shown. One is drawn at random. The probability of blue is .
Answer in simplest form
Show the answer and working
Answer: 16
There are 3 + 1 + 2 = 6 balls, 1 of them blue: 16 = 16.
Example 2
A whole number from 1 to 20 is chosen at random. The probability of a multiple of 4 is .
Answer in simplest form
Show the answer and working
Answer: 14
20 ÷ 4 has whole part 5, so there are 5 multiples of 4: 520 = 14.
Example 3
A box holds 3 red balls and 7 blue ones. One is drawn at random. What is the probability of red?
- A. 37
- B. 710
- C. 110
- D. 310
Choose the right answer
Show the answer and working
Answer: D. 310
There are 10 balls, 3 of them red: P(red) = 310.

Practice questions to try

Try these 5; the answers are at the end. For a whole worksheet, see VIP worksheets below.

1.May rolls a fair die. The probability of a number greater than 1 is .
Answer in simplest form
Answer:
2.A bag holds 5 red balls (R), 1 blue (B) and 1 yellow (Y), as shown. One is drawn at random. The probability of blue is .
Answer in simplest form
Answer:
3.A box holds 7 red balls and 6 blue ones. One is drawn at random. What is the probability of red?
- A. 713
- B. 613
- C. 113
- D. 76
Choose the right answer
Answer:
4.A spinner has 7 equal parts with the numbers shown. Spun once, the probability it stops on an odd number is .
Answer in simplest form
Answer:
5.A whole number from 1 to 18 is chosen at random. The probability of a multiple of 4 is .
Answer in simplest form
Answer:

All the answers

1. 56
2. 17
3. A. 713
4. 47
5. 29

Free worksheet: Equally likely outcomesWorking out, multiple choice and word problems, with answers and working, to print or save as a PDF

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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