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Probability of an event from its intersection with an independent event, and the probability of their union

Probability of an event from its intersection with an independent event, and the probability of their union

6 marks

It is given that \(\mathrm{P}(G)=\dfrac35\) and \(\mathrm{P}(G\cap H)=\dfrac14\), where \(G\) and \(H\) are independent events. Find

  1. \(\mathrm{P}(H)\),
  2. \(\mathrm{P}(G\cup H)\).

[6]

Solution:

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Answer:(a) \(\dfrac{5}{12}\) (b) \(\dfrac{23}{30}\)

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