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Basic Probability Rules

  • If an event \(A\), is certain to happen the probability is equal to \(1\). \(P(A) = 1\) (e.g. the sun will rise tomorrow)
  • If an event \(B\) will never happen, the probability is equal to \(0\). \( P(B)=0\) (e.g. the sun will set in the east today)
  • Complementary events: if \(A\) denotes the event ‘getting rain’, then \(\bar{A}\) denotes the event ‘getting no rain’ and
    \[P(A) + P(\bar{A}) = 1\]
  • That is the sum of the probability of each event occurring is equal to one.
  • Addition rule: if A and B represent two mutually exclusive events (i.e. we can't have situations where they both occur) then 
    \[P(A \mbox{ or } B) = P(A) + P(B)\] 


  • If there the events are not mutually exclusive, then 
    \[P(A \mbox{ or } B) = P(A) + P(B) - P(A \mbox{ and } B)\]

  • Multiplication rule: if \(A\) and \(B\) represent two independent events (i.e. the occurrence of \(A\) will not influence the occurrence of \(B\)) then \[P(A \mbox{ and } B) = P(A)\times P(B)\]

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