Find P(A ∩ B′ ).

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

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]