# Conditional probability

## Main Question or Discussion Point

Hallow! May any one please help me on conditional probability i actualy understand how it occurs but the formula? The logic behind it!

ie P(A/B)=P(AnB)/P(B)

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Hey!

you mean P(A|B) right? P(A/B) could be mistaken for P(A\B) ..the difference.

Anyways, the concept behind this definition (debatably an axiom), is very simple.

Imagine a Venn Diagram with A and B as two circles crossing each other giving rise to a shared mid-section.

P(A) = [outcomes that give event A] divided by [the sample space $$\Omega$$] (all possible outcomes)

P(B) = [outcomes that give event B] divided by [the sample space $$\Omega$$] (all possible outcomes)

P(AnB) = [outcomes that are SHARED between A and B] divided by [the sample space $$\Omega$$] (all possible outcomes)

When they ask you for P(A|B), what they are asking you is:

"what is the probability that A will happen given that we KNOW that B has happened". If we know that the circle B has been chosen the only part of A left that COULD happen is the intersection between A and B that they both share!

Basically: P(A|B) = "what is the probability of A, considering that the ONLY available sample space is now B?"

do you get it now? try and draw it out!

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