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  • STA256 Lecture 03

Multiplication Law of Probability

• The probability of the intersection of two events
• $P(A\cap B)=P(A)P(B|A)=P(B)P(A|B)$
• Proof:
  • RHS
    • $P(A)\cdot P(B|A)$
    • $P(A)\cdot \frac{P(B\cap A)}{P(A)}$
    • $P(B\cap A)=P(A\cap B)$
  • RHS is LHS so proven.