| 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(A ∩ B′ ).
[2]
a.
Given that P((A ∪ B)′ ) = 0.19, find P(A | B′ ).
[4]
b.
Markscheme
valid approach
eg Venn diagram, P(A) − P (A ∩ B), 0.62 − 0.18 (M1)
P(A ∩ B' ) = 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.
