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SL 4.6—Venn diagrams - IB Questionbank | RevisionDojo

Practice SL 4.6—Venn diagrams with authentic IB Mathematics Applications & Interpretation (AI) exam questions for both SL and HL students. This question bank mirrors Paper 1, 2, 3 structure, covering key topics like core principles, advanced applications, and practical problem-solving. Get instant solutions, detailed explanations, and build exam confidence with questions in the style of IB examiners.

Paper

Level

Question 1

HLPaper 2

Consider two events $A$ and $B$ such that $P(A) = k$ , $P(B) = 3k$ , $P(A \cap B) = k^2$ and $P(A \cup B) = 0.5$ .

Calculate $k$ .

[3]

Find $P(A' \cap B)$ .

[3]

Question 2

SLPaper 1

Events $A$ and $B$ are independent with $\text{P}(A \cap B) = 0.2$ and $\text{P}(A' \cap B) = 0.6$ .

Find $\text{P}(B)$ .

[2]

Find $\text{P}(A \cup B)$ .

[4]

Question 3

HLPaper 2

At Mirabooka Primary School, a survey found that 68% of students have a dog and 36% of students have a cat. 14% of students have both a dog and a cat. This information can be represented in the following Venn diagram, where m, n, p and q represent the percentage of students within each region.

Find the value of m.

[2]

Find the value of n.

[1]

Find the value of p.

[2]

Find the value of q.

[1]

Find the probability that a randomly chosen student has a dog but does not have a cat.

[2]

Find the probability that a randomly chosen student has a dog given that they do not have a cat.

[2]

Tim models the number of school captains appointed in the next 10 years who have a dog using a binomial distribution. Assume one school captain is appointed each year. Use Tim's model to find the probability that in the next 10 years 5 school captains have a dog.

[2]

Use Tim's model to find the probability that in the next 10 years more than 3 school captains have a dog.

[3]

Use Tim's model to find the probability that in the next 10 years exactly 9 school captains in succession have a dog.

[2]

10.

State why Tim should not use the binomial distribution to find the probability that 5 school captains have a dog.

[1]

Question 4

SLPaper 1

Consider the following sets:

The universal set $U$ consists of all positive integers less than 15;
$A$ is the set of all numbers which are multiples of 3;
$B$ is the set of all even numbers.

Write down the elements that belong to $A \cap B$.

[3]

Write down the elements that belong to $A \cap B'$.

[2]

Write down $n(A \cap B')$.

[1]

Paper

Level

Question 1

HLPaper 2

Consider two events $A$ and $B$ such that $P(A) = k$ , $P(B) = 3k$ , $P(A \cap B) = k^2$ and $P(A \cup B) = 0.5$ .

Calculate $k$ .

[3]

Find $P(A' \cap B)$ .

[3]

Question 2

SLPaper 1

Events $A$ and $B$ are independent with $\text{P}(A \cap B) = 0.2$ and $\text{P}(A' \cap B) = 0.6$ .

Find $\text{P}(B)$ .

[2]

Find $\text{P}(A \cup B)$ .

[4]

Question 3

HLPaper 2

Find the value of m.

[2]

Find the value of n.

[1]

Find the value of p.

[2]

Find the value of q.

[1]

Find the probability that a randomly chosen student has a dog but does not have a cat.

[2]

Find the probability that a randomly chosen student has a dog given that they do not have a cat.

[2]

Use Tim's model to find the probability that in the next 10 years more than 3 school captains have a dog.

[3]

Use Tim's model to find the probability that in the next 10 years exactly 9 school captains in succession have a dog.

[2]

10.

State why Tim should not use the binomial distribution to find the probability that 5 school captains have a dog.

[1]

Question 4

SLPaper 1

Consider the following sets:

The universal set $U$ consists of all positive integers less than 15;
$A$ is the set of all numbers which are multiples of 3;
$B$ is the set of all even numbers.

Write down the elements that belong to $A \cap B$.

[3]

Write down the elements that belong to $A \cap B'$.

[2]

Write down $n(A \cap B')$.

[1]

Paper

Level

Question 1

HLPaper 2

Consider two events $A$ and $B$ such that $P(A) = k$ , $P(B) = 3k$ , $P(A \cap B) = k^2$ and $P(A \cup B) = 0.5$ .

Calculate $k$ .

[3]

Find $P(A' \cap B)$ .

[3]

Question 2

SLPaper 1

Events $A$ and $B$ are independent with $\text{P}(A \cap B) = 0.2$ and $\text{P}(A' \cap B) = 0.6$ .

Find $\text{P}(B)$ .

[2]

Find $\text{P}(A \cup B)$ .

[4]

Question 3

HLPaper 2

Find the value of m.

[2]

Find the value of n.

[1]

Find the value of p.

[2]

Find the value of q.

[1]

Find the probability that a randomly chosen student has a dog but does not have a cat.

[2]

Find the probability that a randomly chosen student has a dog given that they do not have a cat.

[2]

Use Tim's model to find the probability that in the next 10 years more than 3 school captains have a dog.

[3]

Use Tim's model to find the probability that in the next 10 years exactly 9 school captains in succession have a dog.

[2]

10.

State why Tim should not use the binomial distribution to find the probability that 5 school captains have a dog.

[1]

Question 4

SLPaper 1

Consider the following sets:

The universal set $U$ consists of all positive integers less than 15;
$A$ is the set of all numbers which are multiples of 3;
$B$ is the set of all even numbers.

Write down the elements that belong to $A \cap B$.

[3]

Write down the elements that belong to $A \cap B'$.

[2]

Write down $n(A \cap B')$.

[1]

SL 4.6—Venn diagrams Questionbank