Probability Formulae

Probability Formulas

1. Probability Range for an event A

\[ = 0 = P(A) = 1 \]

2. Rule of Complementary Events

\[ = P(A^c) + P(A) = 1 \]

3. Rule of Addition for events A and B

\[ P(A or B) = P(A) + P(B) – P(A \cap B) \]

4. Disjoint Events
Events A and B are disjoint

\[ <=> P(A\cap B) = 0 \]

5. Conditional Probability i-e probability of event A subject to event B

\[ P(\frac{A}{B}) = \frac{P(A\cap B)} { P(B)} \]

6. Baye’s Formula is

\[ P(\frac{A}{B}) = P(\frac{B}{A})\times \frac{  P(A)}{ P(B)} \]

7. Independent Events
Events A and B are independent if and only if

\[ P(A\cap B) = P(A) \times P(B) \]

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