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Date May 2014 Marks available 2 Reference code 14M.2.sl.TZ2.4
Level SL only Paper 2 Time zone TZ2
Command term Find Question number 4 Adapted from N/A

Question

Let \(A\) and \(B\) be independent events, where \({\text{P}}(A) = 0.3\) and \({\text{P}}(B) = 0.6\).

Find \({\text{P}}(A \cap B)\).

[2]
a.

Find \({\text{P}}(A \cup B)\).

[2]
b.

On the following Venn diagram, shade the region that represents \(A \cap B'\).

[1]
c(i).

Find \({\text{P}}(A \cap B')\).

[2]
c(ii).

Markscheme

correct substitution     (A1)

eg     \(0.3 \times 0.6\)

\({\text{P}}(A \cap B) = 0.18\)     A1     N2

[2 marks]

a.

correct substitution     (A1)

eg   \({\text{P}}(A \cup B) = 0.3 + 0.6 - 0.18\)

\({\text{P}}(A \cup B) = 0.72\)     A1     N2

[2 marks]

b.

     A1     N1

c(i).

appropriate approach     (M1)

eg     \(0.3 - 0.18,{\text{ P}}(A) \times {\text{P}}(B')\)

\({\text{P}}(A \cap B') = 0.12\)   (may be seen in Venn diagram)     A1     N2

[2 marks]

c(ii).

Examiners report

[N/A]
a.
[N/A]
b.
[N/A]
c(i).
[N/A]
c(ii).

Syllabus sections

Topic 5 - Statistics and probability » 5.6 » Combined events, \(P\left( {A \cup B} \right)\) .
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