2025 MI P2 Q8

2025 MI P2 Q8

8 marks

For events \(A\) and \(B\), it is given that \(\mathrm{P}(A) = \frac{11}{20}\), \(\mathrm{P}(A \cup B) = \frac{4}{5}\) and \(\mathrm{P}(B|A) = \frac{4}{11}\).

  1. Find
    1. \(\mathrm{P}(B)\),[3]
    2. \(\mathrm{P}(A \cap B')\).[1]
  2. Determine if the events \(A\) and \(B'\) are mutually exclusive.[1]

A third event \(C\) is such that \(\mathrm{P}(C) = 0.6\) and \(B\) and \(C\) are independent.

  1. Find \(\mathrm{P}(B \cap C)\).[1]
  2. Find the range of values of \(\mathrm{P}(A \cap B' \cap C)\).[2]

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Answer:(i)(a) \(\mathrm P(B)=\dfrac9{20}\) (b) \(\mathrm P(A\cap B')=\dfrac7{20}\) (ii) Not mutually exclusive (iii) \(\mathrm P(B\cap C)=0.27\) (iv) \(0.13\leq\mathrm P(A\cap B'\cap C)\leq0.33\)

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