# Worksheet: Calculating Probability Using Venn Diagrams

In this worksheet, we will practice using Venn diagrams to organize information and calculate probabilities.

**Q1: **

In sample space , for events and , what is the set of outcomes for the event ?

- A{3, 6, 9, 15}
- B{1, 2, 4, 5, 7, 8, 10, 11, 13, 14}
- C{4, 8, 12}
- D{3, 6, 9, 12, 15}
- E{3, 4, 6, 8, 9, 12, 15}

**Q2: **

In sample space , for events and , what is the set of outcomes for the event ?

- A{12}
- B{1, 2, 3, 5, 6, 7, 9, 10, 11, 13, 14, 15}
- C{1, 2, 3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15}
- D{3, 4, 6, 8, 9, 12, 15}
- E{3, 4, 6, 8, 9, 15}

**Q3: **

In sample space , for events and , what is the set of outcomes for the event ?

- A{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15}
- B{3, 6, 9, 15}
- C{3, 4, 6, 8, 9, 12, 15}
- D{12}
- E{1, 2, 5, 7, 10, 11, 13, 14}

**Q4: **

A survey was conducted on a group of 263 children to determine their favorite superheroes. The results are shown in the Venn Diagram. Find .

- A
- B
- C
- D
- E

**Q5: **

In sample space , for events and , what is the set of outcomes for the event ?

- A{1, 2, 3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15}
- B{1, 2, 5, 7, 10, 11, 13, 14}
- C{1, 2, 3, 5, 6, 7, 9, 10, 11, 13, 14, 15}
- D{3, 6, 9, 15}
- E{3, 4, 6, 8, 9, 12, 15}

**Q6: **

The given Venn diagram represents the probabilities of events and .

Find an expression for .

- A
- B
- C
- D
- E

Find an expression for .

- A
- B
- C
- D
- E

Find an expression for .

- A
- B
- C
- D
- E

Hence, determine a formula for in terms of , , and .

- A
- B
- C
- D
- E

**Q7: **

Use the diagram of the sample space to determine .

- A
- B0
- C
- D

**Q8: **

In sample space , for events and , what is the set of outcomes for the event ?

- A{1, 2, 5, 7, 10, 11, 12, 13, 14}
- B{1, 2, 5, 7, 10, 11, 13, 14}
- C{3, 4, 6, 8, 9, 15}
- D{3, 4, 6, 8, 9, 12, 15}
- E{1, 2, 5, 7, 10, 11, 13, 14}

**Q9: **

271 students voted for the types of music they wanted at the school dance. The results are shown in the Venn diagram. Find the probability that a randomly selected student voted for rock and not jazz.

- A
- B
- C
- D
- E

**Q10: **

In sample space , for events and , what is the set of outcomes for the event ?

- A{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15}
- B{1, 2, 5, 7, 10, 11, 13, 14}
- C{1, 2, 3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15}
- D{1, 2, 5, 7, 10, 11, 12, 13, 14}
- E{1, 2, 4, 5, 7, 8, 10, 11, 12, 13, 14}

**Q11: **

Isabella has drawn this Venn Diagram to record the result of randomly selecting a number between 1 and 12.

What is the probability of selecting a number that is a factor of 20? Give your answer as a fraction in its simplest form.

- A
- B
- C
- D
- E

What is the probability of selecting a number that is a factor of 20 and a multiple of 3? Give your answer as a fraction in its simplest form.

What is the probability of selecting a number that is not a multiple of 3? Give your answer as a fraction in its simplest form.

- A
- B
- C0
- D
- E

**Q12: **

The figure shows a Venn diagram with the probabilities given for events and .

Work out .

Work out .

Work out .

**Q13: **

In sample space , for events and , what is the set of outcomes for the event ?

- A{1, 2, 3, 5, 6, 7, 9, 10, 11, 13, 14, 15}
- B{4, 8, 12}
- C{1, 2, 4, 5, 7, 8, 10, 11, 13, 14}
- D{3, 6, 9, 15}
- E{1, 2, 3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15}

**Q14: **

In sample space , for events and , what is the set of outcomes for the event ?

- A
- B
- C
- D
- E

**Q15: **

In sample space , for events and , what is the set of outcomes for the event ?

- A{1, 2, 5, 7, 10, 11, 13, 14}
- B{3, 4, 6, 8, 9, 15}
- C{12}
- D{4, 8, 12}
- E{4, 8}

**Q16: **

In sample space , for events and , what is the set of outcomes for the event ?

- A{4, 8}
- B{1, 2, 5, 7, 10, 11, 13, 12, 14}
- C{1, 2, 5, 7, 10, 11, 13, 14}
- D{4, 8, 12}
- E{3, 6, 9, 15}

**Q17: **

At a restaurant, 34 of the guests ordered a meat main course and 26 ordered a vegetarian main course. 27 people also ordered a dessert; 11 of them had ordered a vegetarian main course.

Which of the following Venn diagrams describes the combinations of meals that were eaten?

- A
- B
- C
- D

Find the probability of a randomly selected guest having a meat main course and no dessert.

Give your answer as a fraction in its simplest form.

- A
- B
- C
- D

**Q18: **

In sample space , for events and , what is the set of outcomes for the event ?

- A{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15}
- B{1, 2, 3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15}
- C{1, 2, 5, 7, 10, 11, 12, 13, 14}
- D{4, 8}
- E{1, 2, 4, 5, 7, 8, 10, 11, 12, 13, 14}

**Q19: **

In sample space , for events and , what is the set of outcomes for the event ?

- A{12}
- B{4, 8, 12}
- C{4, 8}
- D{3, 6, 9, 15}
- E{3, 4, 6, 8, 9, 12, 15}