Probability from two-way tables

The Maths Habit

How could you sort these shapes into groups?

By shape: circles and squares.By pattern: striped and plain.Or both at once, in a two-way table.

The table shows how 30 students travel to school.

	Walk	Bus	Total
Boys	8	6	14
Girls	9	7	16
Total	17	13	30

How many girls walk?9
How many boys are there?14
How many students altogether?30

Two-way table: A table that sorts things two ways at once.
Total: All of them added together.
At random: Without looking, so each one has the same chance.
Probability: How likely something is to happen. It is a number from 0 to 1.

	Striped	Plain	Total
Circle	3	3	6
Square	2	2	4
Total	5	5	10

Find P(girl who walks).

	Walk	Bus	Total
Boys	6	8	14
Girls	7	4	11
Total	13	12	25

P =the ones you wanteveryone

1Find the total for everyone.It is in the corner, where the two Totals meet. It goes on the bottom.
2Find the ones you want.Go along their row and down their column. It goes on the top.
3Write the fraction.Put the top over the bottom.

One student is picked at random. Find P(girl who walks).

	Walk	Bus	Total
Boys	6	8	14
Girls	7	4	11
Total	13	12	25

1Find the total for everyone.

25

2Find the ones you want.

7

3Write the fraction.

P =725

One person is picked at random. Find P(child who swims).

	Swim	Gym	Total
Adults	9	4	13
Children	7	10	17
Total	16	14	30

1Find the total for everyone.

30

2Find the ones you want.

7

3Write the fraction.

P =730

One student is picked at random. Find P(girl who walks).

	Walk	Bus	Total
Boys	6	8	14
Girls	7	4	11
Total	13	12	25

1Find the total for everyone.

25

2Find the ones you want.

7

3Write the fraction.

P =725

1Find the total for everyone.2Find the ones you want.3Write the fraction.

One student is picked at random. Find P(Year 8 who walks).

	Walk	Bus	Total
Year 7	5	8	13
Year 8	9	7	16
Total	14	15	29

1Find the total for everyone.

29

2Find the ones you want.

9

3Write the fraction.

P =929

One student is picked at random. Find P(girl who walks).

	Walk	Bus	Total
Boys	6	8	14
Girls	7	4	11
Total	13	12	25

1Find the total for everyone.

25

2Find the ones you want.

7

3Write the fraction.

P =725

1Find the total for everyone.2Find the ones you want.3Write the fraction.

One person is picked at random. Find P(man who chose tea).

	Tea	Coffee	Total
Men	11	6	17
Women	4	9	13
Total	15	15	30

1Find the total for everyone.

30

2Find the ones you want.

11

3Write the fraction.

P =1130

One student is picked at random. Find P(girl who walks).

	Walk	Bus	Total
Boys	6	8	14
Girls	7	4	11
Total	13	12	25

1Find the total for everyone.

25

2Find the ones you want.

7

3Write the fraction.

P =725

1Find the total for everyone.2Find the ones you want.3Write the fraction.

One student is picked at random. Find P(girl with a dog).

	Cat	Dog	Total
Boys	7	3	10
Girls	8	5	13
Total	15	8	23

1Find the total for everyone.

23

2Find the ones you want.

5

3Write the fraction.

P =523

1Find the total for everyone.2Find the ones you want.3Write the fraction.

1One student is picked at random. Find P(boy who runs).

	Swim	Run	Total
Boys	4	7	11
Girls	9	5	14
Total	13	12	25

1Find the total for everyone.

25

2Find the ones you want.

7

3Write the fraction.

P =725

2One person is picked at random. Find P(adult who walked).

	Walk	Car	Total
Adults	13	5	18
Children	6	9	15
Total	19	14	33

1Find the total for everyone.

33

2Find the ones you want.

13

3Write the fraction.

P =1333

3One student is picked at random. Find P(boy with a dog).

	Cat	Dog	Total
Boys	3	8	11
Girls	10	6	16
Total	13	14	27

1Find the total for everyone.

27

2Find the ones you want.

8

3Write the fraction.

P =827

One student is picked at random. Find P(girl).

	Walk	Bus	Total
Boys	6	8	14
Girls	7	4	11
Total	13	12	25

1Find the total for everyone.

25

2Find the ones you want.

11

3Write the fraction.

P =1125

One student is picked at random. Find P(hot lunch).

	Hot	Cold	Total
Year 9	8	5	13
Year 10	9	7	16
Total	17	12	29

1Find the total for everyone.

29

2Find the ones you want.

17

3Write the fraction.

P =1729

One student is picked at random. Find P(girl).

	Walk	Bus	Total
Boys	6	8	14
Girls	7	4	11
Total	13	12	25

1Find the total for everyone.

25

2Find the ones you want.

11

3Write the fraction.

P =1125

1Find the total for everyone.2Find the ones you want.3Write the fraction.

One person is picked at random. Find P(woman).

	Tea	Coffee	Total
Men	11	6	17
Women	4	9	13
Total	15	15	30

1Find the total for everyone.

30

2Find the ones you want.

13

3Write the fraction.

P =1330

One student is picked at random. Find P(girl).

	Walk	Bus	Total
Boys	6	8	14
Girls	7	4	11
Total	13	12	25

1Find the total for everyone.

25

2Find the ones you want.

11

3Write the fraction.

P =1125

1Find the total for everyone.2Find the ones you want.3Write the fraction.

One student is picked at random. Find P(cat owner).

	Cat	Dog	Total
Boys	7	3	10
Girls	8	5	13
Total	15	8	23

1Find the total for everyone.

23

2Find the ones you want.

15

3Write the fraction.

P =1523

One student is picked at random. Find P(girl).

	Walk	Bus	Total
Boys	6	8	14
Girls	7	4	11
Total	13	12	25

1Find the total for everyone.

25

2Find the ones you want.

11

3Write the fraction.

P =1125

1Find the total for everyone.2Find the ones you want.3Write the fraction.

One student is picked at random. Find P(Year 8).

	Chess	Art	Total
Year 7	6	7	13
Year 8	9	5	14
Total	15	12	27

1Find the total for everyone.

27

2Find the ones you want.

14

3Write the fraction.

P =1427

Probability from two-way tables worksheet, page 1

Probability from two-way tables worksheet, page 2

Answer sheet

Is it right?
Thumbs up: right. Thumbs down: wrong.

	Walk	Bus	Total
Boys	8	6	14
Girls	9	7	16
Total	17	13	30

P(girl who walks) = 930Right
P(girl who walks) = 916Wrong: the bottom is 30
P(boy) = 1430Right
P(bus) = 1316Wrong: the bottom is 30
P(boy who takes the bus) = 306Wrong: upside down

Use the table from the last slide. Write P(girl who walks) = 930 in its simplest form.
310
Use the same table. Find P(does not walk).
1330
Another table shows 50 students. P(Year 8 who cycles) = 15. How many Year 8 students cycle?
10

One student is picked at random. Find P(girl who swims).
925
Use the same table. Find P(boy).
1325
Use the same table. Find P(boy who runs).
825

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