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Date November 2018 Marks available 3 Reference code 18N.1.AHL.TZ0.H_1
Level Additional Higher Level Paper Paper 1 Time zone Time zone 0
Command term Show that Question number H_1 Adapted from N/A

Question

Consider two events, A and B , such that P ( A ) = P ( A B ) = 0.4  and  P ( A B ) = 0.1 .

By drawing a Venn diagram, or otherwise, find P ( A B ) .

[3]
a.

Show that the events A and B are not independent.

[3]
b.

Markscheme

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

        (M1)

Note: Award M1 for a Venn diagram with at least one probability in the correct region.

 

EITHER

P ( A B ) = 0.3      (A1)

P ( A B ) = 0.3 + 0.4 + 0.1 = 0.8      A1

OR

P ( B ) = 0.5      (A1)

P ( A B ) = 0.5 + 0.4 0.1 = 0.8      A1

 

[3 marks]

a.

METHOD 1

P ( A ) P ( B ) = 0.4 × 0.5         (M1)

= 0.2      A1

statement that their  P ( A ) P ( B ) P ( A B )       R1

Note: Award R1 for correct reasoning from their value.

⇒  A , B not independent     AG

 

METHOD 2

P ( A | B ) = P ( A B ) P ( B ) = 0.1 0.5         (M1)

= 0.2      A1

statement that their P ( A | B ) P ( A )       R1

Note: Award R1 for correct reasoning from their value.

⇒  A , B not independent     AG

Note: Accept equivalent argument using  P ( B | A ) = 0.25 .

 

[3 marks]

b.

Examiners report

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

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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