Calculating probability of an event

Nyasha

1. The problem statement, all variables and given/known data
Find the probability of the following statement :

[tex]P(A\prime \cap C | B \prime )[/tex]



2. The attempt at a solution

[tex]P(A \prime \cap C | B\prime ) =\frac{P ( A \prime \cap C \cap B \prime)}{P(B \prime)}= \frac{P ( A \prime \cap C \cap B \prime)}{1-P(b)}[/tex]

I am stuck as to how do l deal with the numerator. Can someone please help me ?

lanedance

what are you trying to do?

Nyasha

I am trying to calculate the probability of [tex]
P(A\prime \cap C | B \prime )
[/tex]. More of like trying to find the algebraic expression to calculate the probability of [tex]
P(A\prime \cap C | B \prime )
[/tex].

lanedance

in terms of what? ie what form are you trying to simplify to/express in?

Nyasha

I am trying to make it as simple as possible so that if given the values of A,B&C you can calculate the probability

lanedance

sorry, its still not clear exactly what you;re trying to do, is this an actual question? given what values?

you will need P(A), P(B), P(C) and some info about their intersections/unions

you could use some basic set theory to re-arrange, but it all depends want you want it in terms of, for example, deriving quickly from venn diagrams

looking at 2 sets A & B
[tex] P(A) + P(B) = P(A \cup B) + P(A \cap B) [/tex]

then adding another set C
[tex] P(A) + P(B) + P(C) = P(A \cup B \cup C) + P(A \cap B) + P(B \cap C) + P(C \cap A) -P(A \cap B \capC) [/tex]