IB Mathematics Analysis and Approaches Topic AHL 4.13—bayes Theorem Questionbank (HL)

IB Mathematics Analysis and Approaches Topic AHL 4.13—bayes Theorem Questionbank (HL) | RevisionDojo

Practice IB Mathematics Analysis and Approaches (AA) Topic AHL 4.13—bayes Theorem with authentic exam-style questions for both SL and HL students. This question bank focuses on the exact syllabus content for AHL 4.13—bayes Theorem and mirrors Paper 1, 2, 3 style where relevant.

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Paper

Level

Question 1

HLPaper 2

A factory has two machines, $A$ and $B$ , producing electrical components. Machine $A$ produces $60%$ of all components and machine $B$ produces $40%$ . Among the components produced by machine $A$ , $5%$ are defective; among those produced by machine $B$ , $3%$ are defective.

Find the probability that a randomly selected component is defective.

[3]

Given that a randomly selected component is defective, find the probability that it was produced by machine $A$ .

[4]

Question 2

HLPaper 1

Males and females were evaluated on a cognitive test of hand-eye coordination for gaming. The results can be seen in the box and whisker plot below.

State the percentage of males have a score lower than the minimum female score.

[1]

Give one similarity and one difference between the data of males and females.

[2]

Assume that $100$ males were tested and $200$ females. A person is selected at random and is known to have a score of $10$ - $13$ . Using the box and whisker plots, show that the probability this person is a female is less than $\frac{2}{3}$ .

[5]

Question 3

HLPaper 2

A factory has three machines $A$ , $B$ and $C$ , producing $40%$ , $35%$ and $25%$ of the total output respectively. The probability that an item is defective is $0.02$ , $0.03$ and $0.06$ for machines $A$ , $B$ and $C$ respectively.

Find the probability that a randomly selected item is defective.

[3]

Given that an item is defective, find the probability that it was produced by machine $C$ .

[3]

Given that an item is not defective, find the probability that it was produced by machine $A$ .

[3]

Two items are selected at random, independently.

Find the probability that exactly one of the two items is defective.

[4]

Question 4

HLPaper 2

In a hospital, three doctors $A$ , $B$ and $C$ see patients in proportions $0.5$ , $0.3$ and $0.2$ respectively. The probability that a patient is correctly diagnosed by doctors $A$ , $B$ and $C$ is $0.92$ , $0.85$ and $0.78$ respectively.

Find the probability that a randomly selected patient is correctly diagnosed.

[4]

Given that a patient is misdiagnosed, find the probability that the patient was seen by doctor $C$ .

[4]

Three patients are independently chosen at random.

Find the probability that exactly two of these patients are correctly diagnosed.

[3]

Ten patients are independently chosen at random.

Find the probability that at least four of these patients are misdiagnosed.

[3]

The hospital sees $1000$ patients in a month, assumed independent.

Find the expected number of patients misdiagnosed in a month.

[3]

The hospital sees $1000$ patients in a month, assumed independent.

Find the standard deviation of the number of patients misdiagnosed in a month.

[3]

Find the smallest integer $n$ such that the probability of obtaining at least one misdiagnosis among $n$ independently chosen patients exceeds $0.999$ .

[4]

Question 5

HLPaper 2

A company manufactures lightbulbs at two factories, $F_{1}$ and $F_{2}$ . Factory $F_{1}$ produces $65%$ of all bulbs and factory $F_{2}$ produces the remaining $35%$ . The lifetime, in hours, of a bulb produced at $F_{1}$ is normally distributed with mean $920$ and standard deviation $110$ . The lifetime, in hours, of a bulb produced at $F_{2}$ is normally distributed with mean $880$ and standard deviation $80$ .

A bulb is considered short-lived if its lifetime is less than $750$ hours.

Twenty bulbs are selected at random.

Find the probability that a bulb produced at $F_{1}$ is short-lived.

[2]

Find the probability that a randomly selected bulb is short-lived.

[4]

A randomly selected bulb is found to be short-lived. Find the probability that it was produced at $F_{1}$ .

[4]

Find the probability that exactly $3$ of them are short-lived.

[3]

Find the expected number of short-lived bulbs in the sample.

[2]

IB Mathematics Analysis and Approaches AHL 4.13—bayes Theorem Questionbank

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IB Mathematics Analysis and Approaches AHL 4.13—bayes Theorem Questionbank

IB Mathematics Analysis and Approaches (AA) Topic AHL 4.13—bayes Theorem Questionbank

Unlock all 16 questions with a free account