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The probability that kebba, Ebou and Omar will hit a target are \(\frac{2}{3}\), \(\frac{3}{4}\) and...

Mathematics
WAEC 2015

The probability that kebba, Ebou and Omar will hit a target are \(\frac{2}{3}\), \(\frac{3}{4}\) and \(\frac{4}{5}\) respectively. Find the probability that only Kebba will hit the target.

  • A. \(\frac{2}{5}\)
  • B. \(\frac{7}{60}\)
  • C. \(\frac{1}{30}\)
  • D. \(\frac{1}{60}\)
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Correct Answer: Option C
Explanation

Pr(Ebou did not hit the target) = 1 - \(\frac{3}{4}\) = \(\frac{1}{4}\) = Pr(E'),  Pr(Omar did not hit the target) = 1 - \(\frac{4}{5}\) = \(\frac{1}{5}\) = Pr(O')

Hence the probability that only Kebba will hit the target

= Pr(K) x Pr(E') x Pr(O')

= \(\frac{2}{3} \times \frac{1}{4} \times \frac{1}{5}\)

= \(\frac{1}{30}\)


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