IB Maths AA HL AA 4.3 Probability questions

Exam-style questions in the shape of Paper 1 and Paper 2, with full markschemes. Read the markscheme, or type, photograph or draw your answer and get it marked.

Question 1

Paper 1, no calculatorEasy5 marks

A clinic records whether each of 100 patients has a particular exposure, EE and whether they have a condition, DD Figure 1 shows the results.

50454035302520151050Number of patientsCondition (D)No condition (D′)Exposed (E)Not exposed (E′)Exposure status
(a)

Write down the formula for P(D∣E)P(D\mid E) assuming P(E)>0P(E)>0

[1]
(b)

Use Figure 1 for both parts.

(i)

Calculate P(D∣E)P(D\mid E)

[2]
(ii)

Determine whether DD and EE are independent. Give a reason.

[2]

Question 2

Paper 1, no calculatorMedium7 marks

A probability tree models the results of a medical study of a risk factor RR and a disease DD A person is selected at random from the population. The probabilities on the second set of branches are conditional on the outcome at the first set of branches.

Selected personRnot RDnot DDnot D154518781403940
(a)

Find the probability that a randomly selected person has both RR and DD

[1]
(b)

Hence determine the probability that a randomly selected person has DD

[2]
(c)

Hence determine the probability that a person has RR given that they have DD Give your answer exactly, and state whether more than half of the people with DD have RR

[4]

Question 3

Paper 1, no calculatorHard6 marks

A health service records whether each of 300 participants has a risk factor FF and whether each is diagnosed with a disease DD Figure 1 shows the results.

020406080100120140160180200220240260Number of participants21624519F presentF absentRisk factor statusDiagnosed with DNot diagnosedwith D

A report notes that more participants diagnosed with DD had FF than did not have FF and concludes that diagnosis is more likely among participants with FF

(a)

State the definition of P(A∣B)P(A\mid B) in terms of P(A∩B)P(A\cap B) and P(B)P(B)

[1]
(b)

Use Figure 1 to calculate P(F∣D)P(F\mid D)

[1]
(c)

In light of your answer to (b), test whether FF and DD are independent and assess the report’s conclusion.

[4]

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