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Stated winning probabilities that do not add up to 1

Stated winning probabilities that do not add up to 1

Secondary 4
6 marks

Exactly one team wins a quiz competition. The probabilities that the Kestrels, the Owls, the Hawks and the Eagles win are \(\dfrac16\), \(\dfrac14\), \(\dfrac18\) and \(\dfrac1{12}\) respectively.

  1. Explain why there must be other teams in the competition.[2]
  2. Find the probability that the Kestrels or the Owls win.[1]
  3. Find the probability that none of the Owls, the Hawks and the Eagles wins.[2]
  4. Find the probability that neither the Kestrels nor the Hawks win.[1]

Solution:

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Answer:(a) Exactly one team wins and the four probabilities add up to \(\frac58<1\), so another team wins with probability \(\frac38\). (b) \(\frac5{12}\) (c) \(\frac{13}{24}\) (d) \(\frac{17}{24}\)

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