All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions.

(i)
\mathrm{P}(B|A') = \frac{\mathrm{P}(B \cap A')}{\mathrm{P}(A')}

0.8 (1- 0.7) = \mathrm{P}(B \cap A')

\mathrm{P}(B \cap A') = 0.24

(ii)
\mathrm{P}(A' \cap B') = P((A \cup B)') = 1 - P(A \cup B)

P(A \cup B) = P(B \cap A') + P(A) = 0.94

\therefore, \mathrm{P}(A' \cap B') = 0.06

(iii)
\mathrm{P}(A|B') = \frac{\mathrm{P}(A \cap B')}{\mathrm{P}(B')}

0.88[\mathrm{P}(A \cap B') + \mathrm{P}(A' \cap B')] = \mathrm{P}(A \cap B')

0.12\mathrm{P}(A \cap B') = 0.0528

\mathrm{P}(A \cap B') = 0.44

\mathrm{P}(A ) = \mathrm{P}(A \cap B) + \mathrm{P}(A \cap B')

\mathrm{P}(A \cap B) = 0.26

KS Comments:

This probability question tests students fully on their ability to manipulate the given probability equations. My advice will always first write out what you know and then attempt to apply the formulas appropriately. Drawing of Venn diagrams are viable but should always be used with care.

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