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

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