Understanding Conditional Probability: Formulas and Logic Explained

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Conditional probability is expressed as P(A|B), which represents the probability of event A occurring given that event B has occurred. The formula P(A|B) = P(A ∩ B) / P(B) illustrates this relationship, where P(A ∩ B) is the probability of both A and B happening together. Visualizing this with a Venn Diagram helps clarify that the relevant sample space is limited to event B, focusing on the intersection of A and B. Understanding this concept involves recognizing that the probability of A is now conditional on the occurrence of B. Drawing out the Venn Diagram can aid in grasping these ideas more clearly.
Godwin Kessy
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Hallow! May anyone 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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