2015 A-level H2 Mathematics (9740) Paper 2 Question 9 Suggested Solutions

By KS Teng

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

(i)
\mathrm{P}(B|A) = \mathrm{P}(B) since A and B are independent.

\therefore, \mathrm{P}(B|A) = \mathrm{P}(B) = 0.4

(ii)
\mathrm{P}(A' \cap B' \cap C')

= 1 - \mathrm{P}(C \cup B \cup A)

= 1 - (0.45 + 0.02 + 0.2 + 0.145)

= 0.185

(iii)

If \mathrm{P}(A' \cap B' \cap C) = 0,

\mathrm{P}(A' \cap B' \cap C')

=1 - [0.935 - (0.3 - 0.035 )]

= 0.33 (maximum)

If \mathrm{P}(A' \cap B \cap C) = 0,

\mathrm{P}(A' \cap B' \cap C')

= 1 - \mathrm{P}(A \cup B \cup C) - 0.22

= 0.165 (minimum)

0.165 \le \mathrm{P}(A' \cap B' \cap C') \le 0.33

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