please help.mutually independent problem

kevek · #1 $Old$ 08-28-2008, 10:23 PM

P(.) is a probability function defined on some sample space, let A,B,C are events.
1)what is meants by saying that A,B,C are mutually independent and mutually disjoint?

2) if A,B,C are mutually independent, why A and B∪ C are independent?

mr fantastic · #2 $Old$ 08-28-2008, 10:33 PM

Quote:

Originally Posted by kevek $View Post$

P(.) is a probability function defined on some sample space, let A,B,C are events.
1)what is meants by saying that A,B,C are mutually independent and mutually disjoint?

2) if A,B,C are mutually independent, why A and B∪ C are independent?

$\Pr(A \cap B \cap C) = \Pr(A) \, \Pr(B) \, \Pr(C)$

$\Pr(A \cap B) = \Pr(A \cap C) = \Pr(B \cap C) = 0$ . In a Venn diagram there is no overlap.

A and B∪ C ...... The symbol between B and C appears as a square to me ....

kevek · #3 $Old$ 08-28-2008, 10:36 PM

Quote:

Originally Posted by mr fantastic $View Post$

$\Pr(A \cap B \cap C) = \Pr(A) \, \Pr(B) \, \Pr(C)$

$\Pr(A \cap B) = \Pr(A \cap C) = \Pr(B \cap C) = 0$ . In a Venn diagram there is no overlap.

A and B∪ C ...... The symbol between B and C appears as a square to me ....

Thank you very much, mr fantastic
There is a union symbol between B and C..

mr fantastic · #4 $Old$ 08-28-2008, 10:57 PM

Quote:

Originally Posted by kevek $View Post$

Thank you very much, mr fantastic
There is a union symbol between B and C..

Use the definition of mutual independence to show that $\Pr(A \cap [B \cup C]) = \Pr(A) \, \Pr(B \cup C)$