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SL 4.11—Conditional and independent probabilities, test for independence - IB Questionbank | RevisionDojo

Practice SL 4.11—Conditional and independent probabilities, test for independence with authentic IB Mathematics Analysis and Approaches (AA) exam questions for both SL and HL students. This question bank mirrors Paper 1, 2, 3 structure, covering key topics like functions and equations, calculus, complex numbers, sequences and series, and probability and statistics. Get instant solutions, detailed explanations, and build exam confidence with questions in the style of IB examiners.

Paper

Level

Question 1

SLPaper 2

A game involves drawing three cards from a standard deck of 52 cards (4 suits, 13 ranks) without replacement. Let A be the event that all three cards are of the same suit, and B be the event that at least two cards are of the same rank.

Find $P(A)$ .

[3]

Find $P(B)$ .

[4]

Find $P(A \cap B)$ , and determine whether A and B are independent.

[5]

Question 2

SLPaper 1

A school has 20 students: 8 take Biology, 7 take Chemistry, and 5 take Physics. Some students take multiple subjects, with 3 taking Biology and Chemistry, 2 taking Biology and Physics, 1 taking Chemistry and Physics, and 1 taking all three. A committee of 4 students is formed randomly.

Find the probability that all 4 students take Biology.

[3]

Find the probability that the committee includes at least one student from each subject.

[5]

Find the probability that all 4 students take at least one of the three subjects.

[4]

Question 3

SLPaper 1

A game involves rolling two fair six-sided dice. Let A be the event that the sum of the dice is 7 , and B be the event that at least one die shows a 4 .

Find $P(A)$ .

[2]

Find $P(B)$ .

[2]

Determine whether events A and B are independent.

[3]

Question 4

SLPaper 1

Let $X$ and $Y$ be two independent events such that $P\left(X \cap Y^{\prime}\right)=0.12$ and $P\left(X^{\prime} \cap Y\right)=0.32$ .

Given that $P(X \cap Y)=k$ , find the value of $k$ .

[4]

Find $P\left(X^{\prime} \cup Y^{\prime}\right)$ . [

[2]

Question 5

SLPaper 1

A factory produces two types of components: Type A and Type B. The probability that a component is Type A is 0.6 . If it is Type A , the probability it is defective is 0.05 ; if it is Type B, the probability it is defective is 0.1 . A quality control test is conducted on components, and if a component is defective, the test detects it with probability 0.9 ; if it is not defective, the test incorrectly flags it as defective with probability 0.02 .

Draw a tree diagram to represent the probabilities of component type, defect status, and test outcome.

[4]

Find the probability that a randomly selected component tests positive for being defective.

[4]

Given that a component tests positive, find the probability that it is actually defective.

[4]

Determine whether the events "component is defective" and "component tests positive" are independent.

[3]

Question 6

SLPaper 1

Let A and B be independent events such that $P(A)=0.6$ and $P(B)=0.4$ .

Find $P(A \cap B)$ .

[2]

Find $P\left(A^{\prime} \cap B^{\prime}\right)$ .

[2]

Find $P(A \cup B)$ .

[2]

Question 7

SLPaper 1

A bag contains 5 red balls ( R ) and 3 blue balls ( B ). Two balls are drawn without replacement.

Complete the tree diagram below by writing probabilities in the spaces provided.

[3]

Find the probability that exactly one ball is red.

[3]

Question 8

SLPaper 1

A survey records whether students in a class prefer tea ( T ) or coffee ( C ). The probability that a student prefers tea is 0.4 , and the probability that they prefer both tea and coffee is 0.15 .

Find the probability that a student prefers coffee.

[3]

Determine whether the events T and C are independent.

[2]

Find the probability that a student prefers tea given that they prefer coffee.

[3]

Question 9

SLPaper 1

A medical test for a disease has a sensitivity of 0.95 (probability of testing positive given the patient has the disease) and a specificity of 0.98 (probability of testing negative given the patient does not have the disease). The disease prevalence in the population is 0.01 . If a patient tests positive, they are given a second independent test with the same sensitivity and specificity.

Find the probability that a randomly selected patient tests positive on the first test.

[3]

Given that a patient tests positive on the first test, find the probability that they have the disease.

[4]

Find the probability that a patient tests positive on both tests.

[4]

Given that a patient tests positive on both tests, find the probability that they have the disease.

[2]

Question 10

SLPaper 1

In a school, there are 15 students in a math club. The teacher needs to select students for various tasks.

Find the number of ways to select 5 students for a competition.

[2]

Find the number of ways to select 10 students for a project.

[2]

Find the number of ways to divide the 15 students into three groups of 5 students each, where the order of groups does not matter.

[3]

SL 4.11—Conditional and independent probabilities, test for independence Questionbank