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Date May 2018 Marks available 2 Reference code 18M.2.sl.TZ1.5
Level SL only Paper 2 Time zone TZ1
Command term Find Question number 5 Adapted from N/A

Question

Two events A and B are such that P(A) = 0.62 and P\(\left( {A \cap B} \right)\) = 0.18.

Find P(AB′ ).

[2]
a.

Given that P((AB)′) = 0.19, find P(A |B).

[4]
b.

Markscheme

valid approach

eg  Venn diagram, P(A) − P (AB), 0.62 − 0.18      (M1)

P(AB' ) = 0.44      A1 N2

[2 marks]

a.

valid approach to find either P(B′ ) or P(B)      (M1)

eg   (seen anywhere), 1 − P(A ∩ B) − P((A ∪ B)′)

correct calculation for P(B′ ) or P(B)      (A1)

eg  0.44 + 0.19, 0.81 − 0.62 + 0.18

correct substitution into \(\frac{{{\text{P}}\left( {A \cap B'} \right)}}{{{\text{P}}\left( {B'} \right)}}\)      (A1)

eg  \(\frac{{0.44}}{{0.19 + 0.44}},\,\,\frac{{0.44}}{{1 - 0.37}}\)

0.698412

P(A |B) = \(\frac{{44}}{{63}}\)  (exact), 0.698     A1 N3

[4 marks]

b.

Examiners report

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

Syllabus sections

Topic 5 - Statistics and probability » 5.5 » Concepts of trial, outcome, equally likely outcomes, sample space ( \(U\) ) and event.

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