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# Probability

### 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 $P(A \mbox{ and } B) = P(A)\times P(B)$