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Probability of an intersection from a given union and under independence

Probability of an intersection from a given union and under independence

6 marks

Two events \(A\) and \(B\) are such that \(P(A)=\dfrac25\) and \(P(B)=\dfrac38\).

Find \(P(A\cap B)\) in each of the following cases.

  1. \(P(A\cup B)=\dfrac{13}{20}\)
  2. \(A\) and \(B\) are independent events.

[6]

Solution:

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Answer:(a) \(\dfrac18\) (b) \(\dfrac{3}{20}\)

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