Probability formulas

Rules

Probability of an event

$\displaystyle P(E) = \frac{\text{favourable outcomes}}{\text{total outcomes}}$

When outcomes are equally likely.

Range

$\displaystyle 0 \le P(E) \le 1$

Complement

$\displaystyle P(E') = 1 - P(E)$

Addition rule

$\displaystyle P(A \cup B) = P(A) + P(B) - P(A \cap B)$

Mutually exclusive events

$\displaystyle P(A \cup B) = P(A) + P(B)$

Only A, not B

$\displaystyle P(A \cap B') = P(A) - P(A \cap B)$