Problem-solving with Venn Diagrams

Explore various Venn diagram problems involving ownership of pets, student studies, probability calculations, and set notation. Understand how to determine the shaded sections in Venn diagrams, calculate the number of people owning both cats and dogs, find the probability of selecting a student studying Drama, and more.

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• Venn diagrams
• Problem-solving
• Probability
• Set notation
• Student studies

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Uploaded on May 12, 2024 | 1 Views

Presentation Transcript

1. Venn Diagrams Venn Diagrams

2. Which of the following represents the shaded section on the Venn diagram? F E A B C D ? ? ? ? ? (? ?)

3. Which of the following represents the shaded section on the Venn diagram? F E A B C D ? ? ? ? ? ? (? ?)

4. In a group of 20 people, 5 own a cat, 9 own a dog and 8 have neither. How many own both a cat and a dog? Dog Cat A B C D 3 6 0 2

5. In a group of 20 people, 5 own a cat, 9 own a dog and 8 have neither. How many own just a cat? Dog Cat A B C D 3 6 0 2

6. There are 90 students in year 11, there are 22 Drama students and 3 times the number of Art students. If 17 students' study both Art and Drama, how many study neither? Drama Art A B C D 19 29 5 12

7. A student either studies Art, Drama, both or neither. What is the probability that a student selected at random studies Drama? Drama Art 29 16 17 28 A B C D 33 90 17 90 33 17

8. If ? = 20 and ? = 17 and ? ? = 3 ? ? if ? ? = ? Write an expression involving ? for the total number of people in the Venn diagram Green Blonde A B C D 37 + ? 37 ? 37 + 4? 37 + 2?

9. Drama Art An Art student is selected at random, what is the probability that they study drama? 29 16 17 28 A B C D 33 90 16 33 16 90 16 45

10. In a Venn diagram ? =numbers 1 to 15 inclusive P = Prime numbers and O = Odd numbers Which Venn Is correct? P P P O O O P O 1 1 1 2 1 2 2 2 9 9 3 9 9 3 3 3 7 7 7 7 5 5 5 5 15 15 15 15 11 11 11 11 13 13 13 13 14 12 4 6 8 10 14 12 4 6 8 10 14 12 4 6 8 10 A B C D