# 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.

• 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}