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Date May 2018 Marks available 3 Reference code 18M.1.SL.TZ2.S_8
Level Standard Level Paper Paper 1 (without calculator) Time zone Time zone 2
Command term Find Question number S_8 Adapted from N/A

Question

Pablo drives to work. The probability that he leaves home before 07:00 is 3 4 .

If he leaves home before 07:00 the probability he will be late for work is 1 8 .

If he leaves home at 07:00 or later the probability he will be late for work is 5 8 .

Copy and complete the following tree diagram.

[3]
a.

Find the probability that Pablo leaves home before 07:00 and is late for work.

[2]
b.

Find the probability that Pablo is late for work.

[3]
c.

Given that Pablo is late for work, find the probability that he left home before 07:00.

[3]
d.

Two days next week Pablo will drive to work. Find the probability that he will be late at least once.

[3]
e.

Markscheme

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

A1A1A1 N3

Note: Award A1 for each bold fraction.

[3 marks]

a.

multiplying along correct branches      (A1)
eg   3 4 × 1 8

P(leaves before 07:00 ∩ late) =  3 32     A1 N2

[2 marks]

b.

 

multiplying along other “late” branch      (M1)
eg   1 4 × 5 8

adding probabilities of two mutually exclusive late paths      (A1)
eg   ( 3 4 × 1 8 ) + ( 1 4 × 5 8 ) , 3 32 + 5 32

P ( L ) = 8 32 ( = 1 4 )     A1 N2

[3 marks]

c.

recognizing conditional probability (seen anywhere)      (M1)
eg  P ( A | B ) , P ( before 7 | late )

correct substitution of their values into formula      (A1)
eg  3 32 1 4

P ( left before 07:00 | late ) = 3 8     A1 N2

[3 marks]

d.

valid approach      (M1)
eg  1 − P(not late twice), P(late once) + P(late twice)

correct working      (A1)
eg   1 ( 3 4 × 3 4 ) , 2 × 1 4 × 3 4 + 1 4 × 1 4

7 16     A1 N2

[3 marks]

e.

Examiners report

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

Syllabus sections

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

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