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Intersection and union of two independent events and a test for mutual exclusivity

Intersection and union of two independent events and a test for mutual exclusivity

6 marks

The events \(C\) and \(D\) are independent, with \(\mathrm{P}(C)=0.45\) and \(\mathrm{P}(D)=0.6\).

  1. Find \(\mathrm{P}(C\cap D)\).[2]
  2. Find \(\mathrm{P}(C\cup D)\).[2]
  3. Determine whether \(C\) and \(D\) are mutually exclusive. Give a reason for your answer.[2]

Solution:

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Answer:(a) \(0.27\) (b) \(0.78\) (c) not mutually exclusive, since \(\mathrm{P}(C\cap D)=0.27\neq0\)

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