# Math Help - proof of independent probability

1. ## proof of independent probability

How can i prove that if 2 events are independent then the probability

P(AnB) = P(A)P(B)????

2. $P (A \cap B) = P(A|B)P(B) = P(A)P(B)$

3. lol ok without using the P(A/B)????

Please prove it WITHOUT the fact the P(A/B) = P(AnB)/P(B)

4. 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

5. 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)..................