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