Probability formulae

1. Unconditional or Marginal Probability
   • Overlapping Events

$$P(A\cap B)=P(A\mid B)P(B)=P(B\mid A)P(A)$$

• Disjoint events

$$P(A\cap B)=0$$

- **Independent events** 

$$P(A\cap B)=P(A)P(B)$$

2. Conditional probability
   • Overlapping events

$$P(A\mid B)=\frac{P(A\cap B)}{P(B)}$$

- **Disjoint Events** 

$$P(A\mid B)=0$$

- **Independent events** 

$$P(A\mid B)=P(A)$$ $$P(A\mid A)=1$$

3. Bayes Rule

$$P(A\mid B)=\frac{P(B\mid A)P(A)}{P(B)}$$