Thread: Probability and Stastistics P(A|B) questions

1. 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)

2. 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 $P(A \cup B) = P(A) + P(B)$.
In general, we know that $P\left( {C|D} \right) = \frac{{P(C \cap D)}}{{P(D)}}$.

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