• Aug 28th 2008, 08:23 PM
kevek
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?
• Aug 28th 2008, 08:33 PM
mr fantastic
Quote:

Originally Posted by kevek
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?

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

\$\displaystyle \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 ....
• Aug 28th 2008, 08:36 PM
kevek
Quote:

Originally Posted by mr fantastic
\$\displaystyle \Pr(A \cap B \cap C) = \Pr(A) \, \Pr(B) \, \Pr(C)\$

\$\displaystyle \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..
• Aug 28th 2008, 08:57 PM
mr fantastic
Quote:

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

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