Instructions
Complete the following exercises related to Venn diagrams, probability, two-way tables, two-step experiments, and data investigation. Answer each question in the space provided.
1. Venn Diagrams
Draw a Venn diagram to represent the following information:
- In a class, 15 students play basketball, 10 students play soccer, and 5 students play both sports.
2. Probability
If you roll a fair six-sided die, what is the probability of rolling:
- a. An even number?
- b. A number greater than 4?
3. Two-Way Tables
Complete the following two-way table based on the data collected from a survey of 30 students about their favorite fruit:
| Favorite Fruit | Likes Apples | Likes Oranges | Total |
|---|---|---|---|
| Male | |||
| Female | |||
| Total | 30 |
4. Two-Step Experiments
A box contains 4 red balls, 3 blue balls, and 2 green balls. You select one ball, record its color, and then select another ball without replacing the first. What is the probability of:
- a. Choosing a red ball first and then a blue ball?
- b. Choosing a green ball first and then a red ball?
5. Investigating Data
Based on the data you collected from your two-way table, answer the following questions:
- a. What is the most popular fruit among the surveyed students?
- b. How many students prefer apples over oranges?
Once you have completed all sections, review your answers and ensure clarity and accuracy. Happy working!