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Question

For any three events A,B and C we have
  • P (at least one of A,B and C occurs)
  • P (at least two of A,B,C occur)
  • P (exactly two of A,B,C occur)
  • P (exactly one of A,B,C occurs)

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Solution

  1. P (at least one of A,B and C occurs)= P(A)+P(B)+P(C)P(AB)P(BC)P(CA)+P(ABC)
  2. P (at least two of A,B and C occurs) =P(BC)+P(CA)+P(AB)2P(ABC)
  3. P (exactly two of A,B and C occurs) =P(BC)+P(CA)+P(AB)3P(ABC)
  4. P (exactly one of A,B and C occurs) =P(A)+P(B)+P(C)2P(BC)2P(CA)2P(AB)+3P(ABC)

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