1. Two Way Tables
L.O. To interpret, construct and find probabilities from a two-way table.
Levels: 5c-6a

2. Year 7 Year 8 Year 9 Boys 14 15 18 Girls 16 13 10 Year 7 Year 8 Year 9
Match the correct two way table with the data used to create it
5C – Interpreting Two Way Tables
Can you match up any extra correct statements with the two way table?
Is there anything else that you can tell from the information given??
Year 7
Year 8
Year 9
Boys 14 15 18
Girls 16 13 10
Year 7
Year 8
Year 9
Boys 11 18 7
Girls 22 14 20
Year 7
Year 8
Year 9
Boys 11 14
Girls 15 9

3. Check your understanding.
Were you able to pair up the statements with the right two way table?
In total, there are more boys than girls in these classes.
There are 10 girls in this teachers Year 9 class.
This teacher has a class with exactly twice as many girls than boys.
One of the classes contained 32 pupils in total.
This teacher has a class that only contains girls.
This teacher has 64 pupils in total in all of their classes.
Year 7
Year 8
Year 9
Boys 14 15 18
Girls 16 13 10
Year 7
Year 8
Year 9
Boys 11 18 7
Girls 22 14 20
Year 7
Year 8
Year 9
Boys 11 14
Girls 15 9

4. Completing Two Way Tables
Sometimes two way tables are incomplete. How could we use the information to fill in the gaps?
Year 7
Year 8
Year 9
TOTAL
Boys 11
Girls 10 43 31 25 85 19 12 42 19 14 29

5. 9 12 29 10 21 19 One for you to do ... Year 7 Year 8 Year 9 TOTAL Boys
Sometimes two way tables are incomplete. How could we use the information to fill in the gaps?
Year 7
Year 8
Year 9
TOTAL
Boys 9 8 12 29
Girls 4 10 7 21 13 18 19 50 9 12 29 10 21 19

6. Using Two Way Tables How can two way tables be useful?
You have this two way table in front of you.
If I was to choose a pupil at random, what is the probability of selecting a Year 8 pupil?
Year 7
Year 8
Year 9
TOTAL
Boys 9 8 12 29
Girls 4 10 7 21 13 18 19 50

7. Using Two Way Tables How can two way tables be useful?
You have this two way table in front of you.
If I was to choose a pupil at random, what is the probability of selecting a Year 8 pupil?
18/50 = 9/25
Year 7
Year 8
Year 9
TOTAL
Boys 9 8 12 29
Girls 4 10 7 21 13 18 19 50

8. Using Two Way Tables How can two way tables be useful?
You have this two way table in front of you.
What is the probability that a pupil selected at random will be a boy?
Year 7
Year 8
Year 9
TOTAL
Boys 9 8 12 29
Girls 4 10 7 21 13 18 19 50

9. Using Two Way Tables How can two way tables be useful?
You have this two way table in front of you.
What is the probability that a pupil selected at random will be a boy?
29/50
Year 7
Year 8
Year 9
TOTAL
Boys 9 8 12 29
Girls 4 10 7 21 13 18 19 50

10. Using Two Way Tables How can two way tables be useful?
You have this two way table in front of you.
If a Year 7 pupil is selected, what is the probability that they will be a girl?
Year 7
Year 8
Year 9
TOTAL
Boys 9 8 12 29
Girls 4 10 7 21 13 18 19 50

11. Using Two Way Tables How can two way tables be useful?
You have this two way table in front of you.
If a Year 7 pupil is selected, what is the probability that they will be a girl?
4/13
Year 7
Year 8
Year 9
TOTAL
Boys 9 8 12 29
Girls 4 10 7 21 13 18 19 50

12. Practice your skills
6C – Complete two way tables and find probabilities.
On your worksheet, complete the two way tables and then answer the questions.
Question 3 is harder than Question 1 or 2. Why?

13. Practice your skills Answers. b) 24/40 = 12/20 = 6/10 = 3/5
Silver
Black
White
Total
Cars 10 7 24
Vans 3 5 8 16 13 12 15 40
b) 24/40 = 12/20 = 6/10 = 3/5
c) 8/40 = 4/20 = 2/10 = 1/5
United
City
Rovers
Total
Boys 24 15 9 48
Girls 10 16 6 32 34 31 80
b) 6/32 = 3/16
c) 24/48 = 1/2
Before 12:30pm
Between 12:30pm and 1pm
After 1pm
Total
Boys 12 5 17
Girls 4 8 3 15 16 13 32
Pink answers are ones you could find from the question.
Blue answers had to be worked out.
b) 4/15
c) 0

14. How to create a two way table
Which two way table represents this information?? In a supermarket survey 30 men and 30 women were asked whether they preferred orange juice or grapefruit juice. 22 men preferred orange juice. 12 women preferred grapefruit juice.

15. How to create a two way table
Which two way table represents this information?? In a supermarket survey 30 men and 30 women were asked whether they preferred orange juice or grapefruit juice. 22 men preferred orange juice. 12 women preferred grapefruit juice. A
Grapefruit Juice
Orange Juice
Men 12 22
Women 18 8

16. How to create a two way table
Which two way table represents this information?? In a supermarket survey 30 men and 30 women were asked whether they preferred orange juice or grapefruit juice. 22 men preferred orange juice. 12 women preferred grapefruit juice. B A
Grapefruit Juice
Orange Juice
Men 13 22
Women 12 9
Grapefruit Juice
Orange Juice
Men 12 22
Women 18 8

17. How to create a two way table
Which two way table represents this information?? In a supermarket survey 30 men and 30 women were asked whether they preferred orange juice or grapefruit juice. 22 men preferred orange juice. 12 women preferred grapefruit juice. B A
Grapefruit Juice
Orange Juice
Men 13 22
Women 12 9
Grapefruit Juice
Orange Juice
Men 12 22
Women 18 8 C
Grapefruit Juice
Orange Juice
Men 8 22
Women 12 18

18. How to create a two way table
Which two way table represents this information?? In a supermarket survey 30 men and 30 women were asked whether they preferred orange juice or grapefruit juice. 22 men preferred orange juice. 12 women preferred grapefruit juice. B A
Grapefruit Juice
Orange Juice
Men 13 22
Women 12 9
Grapefruit Juice
Orange Juice
Men 12 22
Women 18 8 D C
Grapefruit Juice
Orange Juice
Men 8 22
Women 12 18
Grapefruit Juice
Orange Juice
Men 8 12
Women 22

19. How to create a two way table
Which two way table represents this information?? In a supermarket survey 30 men and 30 women were asked whether they preferred orange juice or grapefruit juice. 22 men preferred orange juice. 12 women preferred grapefruit juice. B A
Grapefruit Juice
Orange Juice
Men 13 22
Women 12 9
Grapefruit Juice
Orange Juice
Men 12 22
Women 18 8 D C
Grapefruit Juice
Orange Juice
Men 8 22
Women 12 18
Grapefruit Juice
Orange Juice
Men 8 12
Women 22

20. How to Create a Two Way Table
Read through all of the information first.
Pick out the different categories – men or women, boys or girls, types of colours, types of food etc.
Set out your table.
Fill in what you know

21. Create a two way table
90 people were asked whether they preferred Soaps, Drama or Crime shows. 12 men said they liked Dramas 33 people in total said they liked Soaps, and 27 of these were women. 25 people in total liked Dramas best. Only 10 women liked Crime shows.

22. Create a two way table
90 people were asked whether they preferred Soaps, Drama or Crime shows. 12 men said they liked Dramas 33 people in total said they liked Soaps, and 27 of these were women. 25 people in total liked Dramas best. Only 10 women liked Crime shows. READ through everything first.

23. Create a two way table
90 people were asked whether they preferred Soaps, Drama or Crime shows. 12 men said they liked Dramas 33 people in total said they liked Soaps, and 27 of these were women. 25 people in total liked Dramas best. Only 10 women liked Crime shows. READ through everything first. Find the CATAGORIES of information

24. Create a two way table
90 people were asked whether they preferred Soaps, Drama or Crime shows. 12 men said they liked Dramas 33 people in total said they liked Soaps, and 27 of these were women. 25 people in total liked Dramas best. Only 10 women liked Crime shows. READ through everything first. Find the CATAGORIES of information

25. Create a two way table
90 people were asked whether they preferred Soaps, Drama or Crime shows. 12 men said they liked Dramas 33 people in total said they liked Soaps, and 27 of these were women. 25 people in total liked Dramas best. Only 10 women liked Crime shows. READ through everything first. Find the CATAGORIES of information. Create your TABLE.

26. Create a two way table
90 people were asked whether they preferred Soaps, Drama or Crime shows. 12 men said they liked Dramas 33 people in total said they liked Soaps, and 27 of these were women. 25 people in total liked Dramas best. Only 10 women liked Crime shows. READ through everything first. Find the CATAGORIES of information. Create your TABLE.  S  D  C
TOTAL  M  W

27. Create a two way table
90 people were asked whether they preferred Soaps, Drama or Crime shows. 12 men said they liked Dramas 33 people in total said they liked Soaps, and 27 of these were women. 25 people in total liked Dramas best. Only 10 women liked Crime shows. READ through everything first. Find the CATAGORIES of information. Create your TABLE. FILL IN what you can.  S  D  C
TOTAL  M  W

28. Create a two way table
90 people were asked whether they preferred Soaps, Drama or Crime shows. 12 men said they liked Dramas 33 people in total said they liked Soaps, and 27 of these were women. 25 people in total liked Dramas best. Only 10 women liked Crime shows. READ through everything first. Find the CATAGORIES of information. Create your TABLE. FILL IN what you can.  S  D  C
TOTAL  M  W

29. Create a two way table
90 people were asked whether they preferred Soaps, Drama or Crime shows. 12 men said they liked Dramas 33 people in total said they liked Soaps, and 27 of these were women. 25 people in total liked Dramas best. Only 10 women liked Crime shows. READ through everything first. Find the CATAGORIES of information. Create your TABLE. FILL IN what you can.  S  D  C
TOTAL  M  W
 90

30. Create a two way table
90 people were asked whether they preferred Soaps, Drama or Crime shows. 12 men said they liked Dramas 33 people in total said they liked Soaps, and 27 of these were women. 25 people in total liked Dramas best. Only 10 women liked Crime shows. READ through everything first. Find the CATAGORIES of information. Create your TABLE. FILL IN what you can.  S  D  C
TOTAL  M  W
 90

31. Create a two way table
90 people were asked whether they preferred Soaps, Drama or Crime shows. 12 men said they liked Dramas 33 people in total said they liked Soaps, and 27 of these were women. 25 people in total liked Dramas best. Only 10 women liked Crime shows. READ through everything first. Find the CATAGORIES of information. Create your TABLE. FILL IN what you can.  S  D  C
TOTAL  M
 12  W
 90

32. Create a two way table
90 people were asked whether they preferred Soaps, Drama or Crime shows. 12 men said they liked Dramas 33 people in total said they liked Soaps, and 27 of these were women. 25 people in total liked Dramas best. Only 10 women liked Crime shows. READ through everything first. Find the CATAGORIES of information. Create your TABLE. FILL IN what you can.  S  D  C
TOTAL  M
 12  W
 90

33. Create a two way table
90 people were asked whether they preferred Soaps, Drama or Crime shows. 12 men said they liked Dramas 33 people in total said they liked Soaps, and 27 of these were women. 25 people in total liked Dramas best. Only 10 women liked Crime shows. READ through everything first. Find the CATAGORIES of information. Create your TABLE. FILL IN what you can.  S  D  C
TOTAL  M
 12  W
 33
 90

34. Create a two way table
90 people were asked whether they preferred Soaps, Drama or Crime shows. 12 men said they liked Dramas 33 people in total said they liked Soaps, and 27 of these were women. 25 people in total liked Dramas best. Only 10 women liked Crime shows. READ through everything first. Find the CATAGORIES of information. Create your TABLE. FILL IN what you can.  S  D  C
TOTAL  M
 12  W
 33
 90

35. Create a two way table
90 people were asked whether they preferred Soaps, Drama or Crime shows. 12 men said they liked Dramas 33 people in total said they liked Soaps, and 27 of these were women. 25 people in total liked Dramas best. Only 10 women liked Crime shows. READ through everything first. Find the CATAGORIES of information. Create your TABLE. FILL IN what you can.  S  D  C
TOTAL  M
 12  W
 27
 33
 90

36. Create a two way table
90 people were asked whether they preferred Soaps, Drama or Crime shows. 12 men said they liked Dramas 33 people in total said they liked Soaps, and 27 of these were women. 25 people in total liked Dramas best. Only 10 women liked Crime shows. READ through everything first. Find the CATAGORIES of information. Create your TABLE. FILL IN what you can.  S  D  C
TOTAL  M
 12  W
 27
 33
 90

37. Create a two way table
90 people were asked whether they preferred Soaps, Drama or Crime shows. 12 men said they liked Dramas 33 people in total said they liked Soaps, and 27 of these were women. 25 people in total liked Dramas best. Only 10 women liked Crime shows. READ through everything first. Find the CATAGORIES of information. Create your TABLE. FILL IN what you can.  S  D  C
TOTAL  M
 12  W
 27
 33
 25
 90

38. Create a two way table
90 people were asked whether they preferred Soaps, Drama or Crime shows. 12 men said they liked Dramas 33 people in total said they liked Soaps, and 27 of these were women. 25 people in total liked Dramas best. Only 10 women liked Crime shows. READ through everything first. Find the CATAGORIES of information. Create your TABLE. FILL IN what you can.  S  D  C
TOTAL  M
 12  W
 27
 33
 25
 90

39. Create a two way table
90 people were asked whether they preferred Soaps, Drama or Crime shows. 12 men said they liked Dramas 33 people in total said they liked Soaps, and 27 of these were women. 25 people in total liked Dramas best. Only 10 women liked Crime shows. READ through everything first. Find the CATAGORIES of information. Create your TABLE. FILL IN what you can. Now fill in the rest…  S  D  C
TOTAL  M
 12  W
 27
 10
 33
 25
 90

40. Create your own two way tables 6A – Problem solving with two way tables
A number of men and women were asked which types of crisps they liked best. A total of twelve people said Plain, of which seven were men.
Six women said Salt and Vinegar.
Fourteen men and twelve women liked Cheese and Onion.
There were 28 men in total.
Q: How many people liked Salt and Vinegar best?
A factory employs 12 supervisors, of which 2 are female. They employ 14 office staff, of which 3 are male, and 120 shop floor workers, of which 38 are female.
Q1: How many employees are there in total?
Q2: What is the probability that a female is a supervisor?

41. Answers 13 people P S + V C + O TOTAL Men 7 14 28 Women 5 6 12 23 13P
S + V
C + O
TOTAL
Men 7 14 28
Women 5 6 12 23 13 26 51 S O SF
TOTAL
Men 10 3 82 95
Women 2 11 38 51 12 14
120
146
146 people
2/51