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Date May 2012 Marks available 3 Reference code 12M.1.sl.TZ1.4
Level SL only Paper 1 Time zone TZ1
Command term Show that and Write down Question number 4 Adapted from N/A

Question

Events A and B are such that \({\rm{P}}(A) = 0.3\) , \({\rm{P}}(B) = 0.6\) and \({\rm{P}}(A \cup B) = 0.7\) .


The values q , r , s and t represent probabilities.

Write down the value of t .

[1]
a.

(i)     Show that \(r = 0.2\) .

(ii)    Write down the value of q and of s .

[3]
b(i) and (ii).

(i)     Write down \({\rm{P}}(B')\) .

(ii)    Find \({\rm{P}}(A|B')\) .

[3]
c(i) and (ii).

Markscheme

\(t = 0.3\)     A1     N1

[1 mark]

a.

(i) correct values     A1

e.g. \(0.3 + 0.6 - 0.7\) , \(0.9 - 0.7\)

\(r = 0.2\)     AG     N0

(ii) \(q = 0.1\) , \(s = 0.4\)     A1A1     N2

[3 marks]

b(i) and (ii).

(i) \(0.4\)     A1     N1

(ii) \({\rm{P}}(A|B') = \frac{1}{4}\)     A2     N2

[3 marks]

c(i) and (ii).

Examiners report

Parts (a), (b), and (c)(i) of this Venn diagram probability question were answered quite well with candidates consistently earning full marks.

a.

Parts (a), (b), and (c)(i) of this Venn diagram probability question were answered quite well with candidates consistently earning full marks. Only a few candidates worked backwards from the \(r = 0.2\) given in the "show that" portion of part (b).

b(i) and (ii).

Many candidates struggled on part (c)(ii), either not recognizing conditional probability or multiplying probabilities to find the numerator as if the events were independent. A number of candidates who successfully found the probability in part (c)(ii) left their incomplete answer of \(\frac{{0.1}}{{0.4}}\) .

c(i) and (ii).

Syllabus sections

Topic 5 - Statistics and probability » 5.5 » The complementary events \(A\) and \({A'}\) (not \(A\)).
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