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The probabilities that Kodjo and Adoga pass an examination are \(\frac{3}{4}\) and ...

The probabilities that Kodjo and Adoga pass an examination are \(\frac{3}{4}\) and \(\frac{3}{5}\) respectively. Find the probability of both boys failing the examination
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  • A \(\frac{1}{10}\)
  • B \(\frac{3}{10}\)
  • C \(\frac{9}{20}\)
  • D \(\frac{2}{3}\)
Correct Answer: Option A
Explanation:
P(Kodjo passing) = \(\frac{3}{4}\); P(Adoga passing) = \(\frac{3}{5}\)
P(Kodjo failing) = \(\frac{1}{4}\); P(Adoga failing) = \(\frac{2}{5}\)
P(both fail) = \(\frac{1}{4} \times \frac{2}{5}\)
= \(\frac{1}{10}\)

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