Two-Way Tables Worksheet

Name:

Date:

🎯 Success Criteria - Check your understanding!

By the end of this lesson, I can:

Create a two-way table from raw data involving two categorical variables

Read and explain the meaning of entries in a two-way table

Calculate probabilities of single and combined events using two-way tables

Use correct probability terminology when explaining my reasoning

📊 Part 1: Constructing Two-Way Tables

1. A survey of 30 Year 10 students asked about their favourite sport and gender. The raw data is shown below:

Data: Male-Football, Female-Basketball, Male-Cricket, Female-Netball, Male-Football, Female-Basketball, Male-Basketball, Female-Netball, Male-Cricket, Female-Football, Male-Football, Female-Basketball, Male-Basketball, Female-Netball, Male-Cricket, Female-Basketball, Male-Football, Female-Netball, Male-Basketball, Female-Basketball, Male-Cricket, Female-Football, Male-Football, Female-Netball, Male-Basketball, Female-Basketball, Male-Cricket, Female-Basketball, Male-Football, Female-Netball

Complete the two-way table below:

2. From the table you created above, what is the total number of students who prefer basketball?

Answer: ____________

3. How many female students were surveyed in total?

Answer: ____________

🎲 Part 2: Calculating Probabilities

Use the two-way table below showing students' favourite fruit by year level:

	Apples	Oranges	Bananas	Total
Year 9	8	12	5	25
Year 10	15	6	9	30
Total	23	18	14	55

4. Calculate the probability that a randomly selected student is from Year 10 and likes apples.

5. What is the probability that a student likes oranges or is from Year 9?

6. Find the probability that a student is not from Year 10.

7. Multiple Choice: Which statement about the data is correct?

More Year 9 students like bananas than Year 10 students

Apples are the most popular fruit overall

Year 10 students prefer oranges to bananas

Equal numbers of students from each year level were surveyed

✏️ Part 3: Analysis and Explanation

8. Look at the fruit preference table above. Describe one relationship you can identify between year level and fruit preference. Use mathematical evidence to support your answer.

9. A student says "The probability of selecting a Year 9 student who likes apples is the same as selecting a Year 10 student who likes oranges." Is this statement correct? Show your working and explain your reasoning using proper probability language.

10. Create your own probability question using the fruit preference table. Then solve it, showing all working.

My question:

Solution: