# Probability and Stastistics P(A|B) questions

• Sep 3rd 2008, 07:18 AM
Dream
Probability and Stastistics P(A|B) questions
Hey guys, I am trying to figure out these two problems, but I cann't really understand what my teacher is asking for. Could someone please help?

1.) Prove each of the following statments, assuming that any conditioning event has positive probability. ( u denotes union, and n denotes intersection)

C) If A and B are mutually exclusive, then
P(A|AuB) = (P(A))/(P(A) + P(B))

D) P(AnBnC) = P(A|BnC)P(B|C)P(C)
• Sep 3rd 2008, 07:41 AM
Plato
Quote:

Originally Posted by Dream
1.) Prove each of the following statments, assuming that any conditioning event has positive probability. ( u denotes union, and n denotes intersection)
C) If A and B are mutually exclusive, then
P(A|AuB) = (P(A))/(P(A) + P(B))
D) P(AnBnC) = P(A|BnC)P(B|C)P(C)

If A and B are mutually exclusive the we know that $\displaystyle P(A \cup B) = P(A) + P(B)$.
In general, we know that $\displaystyle P\left( {C|D} \right) = \frac{{P(C \cap D)}}{{P(D)}}$.

$\displaystyle P(A \cap B \cap C) = P(A|B \cap C)P(B \cap C) = P(A|B \cap C)P(B|C)P(C)$