Two way tables Quiz (Grade 3)

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Score: 0 / 10

Two way tables — Notes & Worked Examples Show / Hide

Explanation:

A two-way table sorts data into rows (one category) and columns (a second category). Every row adds across to its Row Total on the right, every column adds down to its Column Total at the bottom, and both sets of totals add to the Grand Total in the bottom-right corner.

Start with any row or column that has only one missing value, subtract from the total to fill it in, and repeat until every cell is complete. Read probability questions carefully to check the denominator.

Example 1: Complete the two-way table for 80 students choosing French or Spanish (bold numbers are the missing answers).

	French	Spanish	Total
Year 10	18	27	45
Year 11	14	21	35
Total	32	48	80

Y10 Spanish = 45 − 18 = 27; Y11 French = 32 − 18 = 14

Y11 Total = 80 − 45 = 35; Spanish Total = 27 + 21 = 48

Example 2: Using the completed table in Example 1:
(a) Find the probability a random student studies Spanish.
(b) A Year 11 student is chosen at random. Find P(French).

Solution:

(a) Out of all 80 students, 48 study Spanish:

P(Spanish) = 4880 = 35

(b) Out of the 35 Year 11s, 14 study French:

Answer: (a) 4880 (b) 1435 (or 25)

One Page Guide (PDF) Two way tables Worksheets

Question 1

[1 mark]

102 students went on a school trip.
Each student went to Theme Park, Zoo, or Museum.
53 of these students were Year 10 the rest were Year 11.
A total of 45 students went to Theme Park.
10 of the 27 students that went to Museum were Year 11.
11 students who went to Zoo were Year 10.
How many Year 10 students went to Theme Park?

Worked Solution & Answer

Draw a two-way table for Year 10/Year 11 and Theme Park/Zoo/Museum. First find Year 10 in Museum using 27 - 10 = 17, then subtract from the Year 10 total 53.
25

Answer: 25

Question 2

[1 mark]

104 students attended a revision lesson at the weekend.
Each student went to Maths, English, or Science.
49 of these students were Saturday the rest were Sunday.
A total of 38 students went to Maths.
16 of the 32 students that went to Science were Sunday.
14 students who went to English were Saturday.
How many Saturday students went to Maths?

Worked Solution & Answer

Draw a two-way table for Saturday/Sunday and Maths/English/Science. First find Saturday in Science using 32 - 16 = 16, then subtract from the Saturday total 49.
19

Answer: 19

Question 3

[3 marks]

James asks students in Year 10 and Year 11 to name their favourite language from
French or German or Spanish.
The two-way table shows information about his results.

Complete the two-way table.

Worked Solution & Answer

Year 10 Total = 207 – 113 = 94 M1
Year 10 German = 94 – 33 – 34 = 27
Total German = 27 + 45 = 72 M1
Year 11 Spanish = 67 – 34 = 33
Year 11 French = 113 – 45 – 33 = 35
Total French = 33 + 35 = 68 A1

Answer: Year 10: 33, 27, 34, 94; Year 11: 35, 45, 33, 113; Total: 68, 72, 67, 207

Question Paper (PDF) • Mark Scheme (PDF)

Question 4

[3 marks]

Vadim has 56 clocks.
The clocks are only red, only blue or only black.

32 of the clocks are plastic.
5 of the 14 blue clocks are plastic.
8 of the 12 red clocks are **not** plastic.
Use this information to complete the two-way table.

Worked Solution & Answer

Red plastic = 12 – 8 = 4 M1
Black plastic = 32 – (4 + 5) = 23
Blue not plastic = 14 – 5 = 9 M1
Black total = 56 – (12 + 14) = 30
Black not plastic = 30 – 23 = 7
Total not plastic = 24 A1

Answer: Plastic: 4, 5, 23, 32; Not plastic: 8, 9, 7, 24; Total: 12, 14, 30, 56

Question Paper (PDF) • Mark Scheme (PDF)

Question 5 Specimen Set 1 1F Q11

[3 marks]

Complete the two-way table.

Worked Solution & Answer

Boys brown = 12 – (5 + 4) = 3 M1
Girls total = 30 – 12 = 18
Girls green = 9 – 4 = 5 M1
Girls blue = 18 – (7 + 5) = 6
Total blue = 5 + 6 = 11
Total brown = 3 + 7 = 10. A1

Answer: Boys brown = 3; Girls: blue = 6, green = 5, total = 18; Total: blue = 11, brown = 10

Question Paper (PDF) • Mark Scheme (PDF)

Question 6 IGCSE Jun 2023 2FR Q11

[3 marks]

180 passengers travelled either to Seoul or to Tokyo.
They travelled either business class or economy class.

Of these 180 passengers
51 travelled business class to Seoul
69 travelled economy class to Tokyo
86 in total travelled business class
Use this information to complete the two-way table.

Worked Solution & Answer

Business Tokyo = 86 – 51 = 35 M1
Total Tokyo = 35 + 69 = 104
Total Seoul = 180 – 104 = 76 M1
Economy Seoul = 76 – 51 = 25
Total Economy = 25 + 69 = 94 A1

Answer: Business: 51, 35, 86; Economy: 25, 69, 94; Total: 76, 104, 180

Question Paper (PDF) • Mark Scheme (PDF)

Question 7

[3 marks]

Sophie works in a bed shop.
During the last three months she sold 198 beds.

59 beds were sold without a mattress.
45 beds were double beds.
17 of the single beds were sold without a mattress.
67 of the 83 king size beds were sold with a mattress.
Use this information to complete the two-way table.

Worked Solution & Answer

With mattress total = 198 – 59 = 139 M1
Single total = 198 – 45 – 83 = 70 M1
Single with mattress = 70 – 17 = 53 A1

Answer: With mattress: 53, 19, 67, 139; Without mattress: 17, 26, 16, 59; Total: 70, 45, 83, 198

Question Paper (PDF) • Mark Scheme (PDF)

Question 8

[3 marks]

Ishmael asked 30 students at college to tell him the sport they each like the best from cricket or tennis or swimming.

11 of the 20 female students said swimming.
2 of the male students said tennis.
5 students said cricket.
The number of male students who said cricket was the same as the number of male students who said swimming.
Complete the two-way table.

Worked Solution & Answer

Male total = 30 – 20 = 10 M1
Male cricket = Male swimming = (10 – 2) ÷ 2 = 4 M1
Female cricket = 5 – 4 = 1
Female tennis = 20 – (1 + 11) = 8 A1

Answer: Male: 4, 2, 4, 10; Female: 1, 8, 11, 20; Total: 5, 10, 15, 30

Question Paper (PDF) • Mark Scheme (PDF)

Question 9 IGCSE Nov 2020 1F Q8

[4 marks]

Pavel asked 60 people at an airport where they came from.
All of the 60 people came from Europe or Africa or Asia.

9 people came from Africa.
14 females came from Europe.
3 males came from Africa.
16 of the 29 males came from Asia.
Using this information, complete the two-way table.

Worked Solution & Answer

Male Europe = 29 − (3 + 16) = 10 M1
Total Europe = 10 + 14 = 24 M1
Female Africa = 9 − 3 = 6
Total Female = 60 − 29 = 31 M1
Female Asia = 31 − (14 + 6) = 11
Total Asia = 16 + 11 = 27 A1

Answer: Male: 10, 3, 16, 29 | Female: 14, 6, 11, 31 | Total: 24, 9, 27, 60

Question Paper (PDF) • Mark Scheme (PDF)

Question 10

[5 marks]

500 people were asked what type of film they liked best.
280 of the 500 people were adults.
100 of the adults said they liked action films best.
80 of the children said they liked thriller films best.
150 of the people said they liked action films best.
200 of the people said they liked comedy films best.

(a) Complete the two-way table. [3 marks]

(b) Find the probability that this person is an adult who said they liked action films best. [2 marks]

Worked Solution & Answer

(a)

Adults: 110, 70, 100, 280 M1
Children: 90, 80, 50, 220 M1
Total: 200, 150, 150, 500 A1

Answer (a): Adults: 110, 70, 100, 280; Children: 90, 80, 50, 220; Total: 200, 150, 150, 500

(b)

100 adults liked action out of 500 people = 100/500 = 1/5 M1 A1

Answer (b): 100500

Question Paper (PDF) • Mark Scheme (PDF)

Score: 0 / 10 (0 / 29 marks)

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Grade 3 Quizzes

24 Topics

3A - Error intervals	3B - Operations with fractions
3C - Estimation	3D - Writing and simplifying ratio
3E - Ratio	3F - Proportion recipes
3G - Percentages	3H - Percentage change
3J - Exchange rates	3K - Conversions and units
3L - Scale drawings	3M - Best buy questions
3N - Substitution	3P - Solving linear equations
3Q - Straight line graphs	3R - Area and circumference
3S - Rotations	3T - Reflections
3U - Enlargements	3V - Translations
3W - Mixed transformations	3X - Area of compound shapes
3Y - Frequency trees	3Z - Two way tables