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Venn Diagrams - Extended Response Questions

Question 1 of 12

The Venn diagram shows the distribution of elements in two sets A and B. Transfer the information in the Venn diagram to a two-way table and find:

i) \(P(A \cap B)\)

ii) \(P(A \cap B')\)

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Venn Diagrams - Extended Response Questions

Question 2 of 12

From a group of 40 adults, 24 enjoy reading crime fiction (C), 14 enjoy reading historical fiction (H) and 6 enjoy reading crime fiction and historical fiction.

a) Illustrate the information on a Venn diagram.

b) Find the probability that a person chosen at random from the group will enjoy reading:

(i) crime fiction (ii) only crime fiction

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Venn Diagrams - Extended Response Questions

Question 3 of 12

The Venn diagram shows the distribution of elements in two sets A and B. Show that:

\(P(A \cup B) = P(A) + P(B) - P(A \cap B)\)

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Venn Diagrams - Extended Response Questions

Question 4 of 12

The adjacent Venn diagram indicates the types of music a group of 40 people enjoy.

C represents Classical, J represents Jazz and B represents Blues.

i) Given that 10 people enjoy Jazz, calculate \(a\) and \(b\).

ii) Find the probability that one of these people enjoy Blues but not Jazz.

Answer

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Venn Diagrams - Extended Response Questions

Question 5 of 12

A class of students study at least one of the languages: Chinese and French. Of the 30 students in the class, 16 study Chinese and 20 study French.

i) What is the probability that a randomly chosen student studies Chinese?

ii) What is the probability that two randomly chosen students both study Chinese?

iii) What is the probability that a randomly chosen student studies only one language?

Answer

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Venn Diagrams - Extended Response Questions

Question 6 of 12

The Venn diagram shows the distribution of elements in two sets \(A\) and \(B\). \({\rm{P}}\left( {{\rm{A'}} \cup {\rm{B'}}} \right) = ?\)

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Venn Diagrams - Extended Response Questions

Question 7 of 12

The Venn diagram shows the distribution of elements of two sets \(A\) and \(B\). \({\rm{P}}\left( {{\rm{A'}} \cap {\rm{B}}} \right) = ?\)

Answer

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Venn Diagrams - Extended Response Questions

Question 8 of 12

The Venn diagram shows the distribution of elements in two sets A and B. \({\rm{P}}\left( {{\rm{A}} \cup {\rm{B}}} \right) = ?\)

A

\(\frac{9}{{11}}\)

B

\(\frac{8}{{11}}\)

C

\(\frac{2}{{9}}\)

D

\(\frac{2}{{11}}\)

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Venn Diagrams - Extended Response Questions

Question 9 of 12

The Venn diagram shows the distribution of elements in two sets A and B. \({\rm{P}}\left( {{\rm{A'}} \cap {\rm{B'}}} \right) = ?\)

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Venn Diagrams - Extended Response Questions

Question 10 of 12

The Venn diagram shows the distribution of elements in two sets A and B. \({\rm{P}}\left( {{\rm{A'}} \cup {\rm{B}}} \right) = ?\)

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Venn Diagrams - Extended Response Questions

Question 11 of 12

The Venn diagram shows the distribution of elements in two sets A and B. \({\rm{P}}\left( {{\rm{A}} \cap {\rm{B}}} \right) = ?\)

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Venn Diagrams - Extended Response Questions

Question 12 of 12

The Venn diagram shows the distribution of elements in two sets A and B. \({\rm{P}}\left( {{\rm{A'}} \cap {\rm{B}}} \right) = ?\)

Answer

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