How can i prove that if 2 events are independent then the probability P(AnB) = P(A)P(B)????
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$\displaystyle P (A \cap B) = P(A|B)P(B) = P(A)P(B) $
lol ok without using the P(A/B)???? Please prove it WITHOUT the fact the P(A/B) = P(AnB)/P(B)
Last edited by mr fantastic; Apr 5th 2010 at 02:50 PM. Reason: Merged posts
Originally Posted by millwallcrazy How can i prove that if 2 events are independent then the probability P(AnB) = P(A)P(B)???? What definition of independence are you using? The above is the definition I would normally use. CB
The three equivalent definitions of independence are P(AB)=P(A)P(B) P(A|B)=P(A) P(B|A)=P(B) If any one holds the other two hold, if any one fails... You can also throw in P(A'|B)=P(A') P(A|B')=P(A)..................
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