18M.2.SL.TZ1.S_5

pestleMathematicsAISLPaper 218M· sl-4-5-probability-concepts-expected-numberssource ↗

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

Find P(A ∩ B′ ).

[2]

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

[4]

Markscheme / solution

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

valid approach

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

P(A ∩ B' ) = 0.44 A1 N2

[2 marks]

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]

Examiners’ report

[N/A]