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 𝑆, for events 𝐴 and 𝐵, what is the set of outcomes for the event 𝐴?

  • 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 𝑆, for events 𝐴 and 𝐵, what is the set of outcomes for the event 𝐴𝐵?

  • 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 𝑆, for events 𝐴 and 𝐵, what is the set of outcomes for the event 𝐴𝐵?

  • 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 𝑃()WonderWomanorBatman.

  • A39263
  • B22263
  • C178263
  • D30263
  • E8263

Q5:

In sample space 𝑆, for events 𝐴 and 𝐵, what is the set of outcomes for the event 𝐴𝐵?

  • 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 𝐴 and 𝐵.

Find an expression for 𝑃(𝐴𝐵).

  • A1(𝑝+𝑞+𝑟)
  • B𝑞
  • C𝑝+𝑞+𝑟
  • D𝑝+𝑟
  • E𝑝

Find an expression for 𝑃(𝐴)+𝑃(𝐵).

  • A𝑝+𝑟
  • B𝑝+𝑞+𝑟
  • C𝑝+2𝑞+𝑟
  • D𝑝𝑞𝑟
  • E𝑞

Find an expression for 𝑃(𝐴𝐵).

  • A𝑞
  • B1𝑞
  • C𝑟
  • D𝑝+𝑟
  • E𝑝+𝑞+𝑟

Hence, determine a formula for 𝑃(𝐴𝐵) in terms of 𝑃(𝐴), 𝑃(𝐵), and 𝑃(𝐴𝐵).

  • A𝑃(𝐴𝐵)=𝑃(𝐴)𝑃(𝐵)𝑃(𝐴𝐵)
  • B𝑃(𝐴𝐵)=𝑃(𝐴)+𝑃(𝐵)2𝑃(𝐴𝐵)
  • C𝑃(𝐴𝐵)=𝑃(𝐴)+𝑃(𝐵)𝑃(𝐴𝐵)
  • D𝑃(𝐴𝐵)=𝑃(𝐴)+𝑃(𝐴𝐵)𝑃(𝐵)
  • E𝑃(𝐴𝐵)=𝑃(𝐵)+𝑃(𝐴𝐵)𝑃(𝐴)

Q7:

Use the diagram of the sample space 𝑆 to determine 𝑃(𝐵𝐶).

  • A310
  • B0
  • C35
  • D12

Q8:

In sample space 𝑆, for events 𝐴 and 𝐵, what is the set of outcomes for the event (𝐴𝐵)?

  • 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.

  • A9271
  • B15271
  • C22271
  • D77271
  • E33271

Q10:

In sample space 𝑆, for events 𝐴 and 𝐵, what is the set of outcomes for the event 𝐴𝐵?

  • 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.

  • A14
  • B13
  • C23
  • D712
  • E512

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.

  • A512
  • B13
  • C0
  • D23
  • E712

Q12:

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

Work out 𝑃(𝐴).

Work out 𝑃(𝐴𝐵).

Work out 𝑃(𝐵𝐴).

Q13:

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

  • 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 𝑆, for events 𝐴 and 𝐵, what is the set of outcomes for the event (𝐴𝐵)?

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

Q15:

In sample space 𝑆, for events 𝐴 and 𝐵, what is the set of outcomes for the event 𝐴𝐵?

  • 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 𝑆, for events 𝐴 and 𝐵, what is the set of outcomes for the event 𝐴𝐵?

  • 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.

  • A310
  • B717
  • C730
  • D917

Q18:

In sample space 𝑆, for events 𝐴 and 𝐵, what is the set of outcomes for the event 𝐴𝐵?

  • 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 𝑆, for events 𝐴 and 𝐵, what is the set of outcomes for the event 𝐴𝐵?

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

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.