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Date May 2019 Marks available 3 Reference code 19M.2.AHL.TZ2.H_3
Level Additional Higher Level Paper Paper 2 Time zone Time zone 2
Command term Label Question number H_3 Adapted from N/A

Question

Iqbal attempts three practice papers in mathematics. The probability that he passes the first paper is 0.6. Whenever he gains a pass in a paper, his confidence increases so that the probability of him passing the next paper increases by 0.1. Whenever he fails a paper the probability of him passing the next paper is 0.6.

Complete the given probability tree diagram for Iqbal’s three attempts, labelling each branch with the correct probability.

[3]
a.

Calculate the probability that Iqbal passes at least two of the papers he attempts.

[2]
b.

Find the probability that Iqbal passes his third paper, given that he passed only one previous paper.

[3]
c.

Markscheme

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

     A1A1A1

Note: Award A1 for each correct column of probabilities.

[3 marks]

a.

probability (at least twice) =

EITHER

(0.6×0.7×0.8)+(0.6×0.7×0.2)+(0.6×0.3×0.6)+(0.4×0.6×0.7)       (M1)

OR

(0.6×0.7)+(0.6×0.3×0.6)+(0.4×0.6×0.7)       (M1)

Note: Award M1 for summing all required probabilities.

THEN

= 0.696     A1

[2 marks]

b.

P(passes third paper given only one paper passed before)

=P(passes third AND only one paper passed before)P(passes once in first two papers)      (M1)

=(0.6×0.3×0.6)+(0.4×0.6×0.7)(0.6×0.3)+(0.4×0.6)      A1

= 0.657     A1

[3 marks]

c.

Examiners report

[N/A]
a.
[N/A]
b.
[N/A]
c.

Syllabus sections

Topic 4—Statistics and probability » SL 4.6—Combined, mutually exclusive, conditional, independence, prob diagrams
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