Conditional Probability, Product Rule, Independent Events, Bayes Theorem

Context:

• Source:
• Relation:

---

Insight:

• Conditional Prob: $P(E|F)=\frac{P(E\cap F)}{P(F)}$
• Product Rule: $P(E\cap F)=P(E)\cdot P(F|E)=P(F)\cdot P(E|F)$
• Inde Events (IE): $P(E|F)=P(E),P(F|E)=P(F)$
• Prove IE/Prod Rule IE: $P(E\cap F)=P(E)\cdot P(F)$
• Bayes: $P(F|E)=\frac{P(F\cap E)}{P(E)}=\frac{P(F)\cdot P(E|F)}{P(F)\cdot P(E|F)+P(F^{\prime })\cdot P(E|F^{\prime })}$