# Calculating probability of an event

## Homework Statement

Find the probability of the following statement :

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

2. The attempt at a solution

$$P(A \prime \cap C | B\prime ) =\frac{P ( A \prime \cap C \cap B \prime)}{P(B \prime)}= \frac{P ( A \prime \cap C \cap B \prime)}{1-P(b)}$$

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

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lanedance
Homework Helper
what are you trying to do?

what are you trying to do?
I am trying to calculate the probability of $$P(A\prime \cap C | B \prime )$$. More of like trying to find the algebraic expression to calculate the probability of $$P(A\prime \cap C | B \prime )$$.

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

in terms of what? ie what form are you trying to simplify to/express in?
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
Homework Helper
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
$$P(A) + P(B) = P(A \cup B) + P(A \cap B)$$

$$P(A) + P(B) + P(C) = P(A \cup B \cup C) + P(A \cap B) + P(B \cap C) + P(C \cap A) -P(A \cap B \capC)$$