Understanding Conditional Probability: Formulas and Logic Explained

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SUMMARY

This discussion clarifies the concept of conditional probability, specifically the formula P(A|B) = P(AnB) / P(B). The distinction between P(A|B) and P(A\B) is emphasized, highlighting the importance of understanding the notation. The explanation utilizes a Venn Diagram to illustrate the relationship between events A and B, focusing on the shared outcomes in the intersection. The key takeaway is that P(A|B) represents the probability of event A occurring given that event B has already occurred.

PREREQUISITES
  • Understanding of basic probability concepts
  • Familiarity with Venn Diagrams
  • Knowledge of sample space and outcomes
  • Ability to interpret mathematical notation in probability
NEXT STEPS
  • Study the derivation of Bayes' Theorem for conditional probabilities
  • Learn about joint probability distributions and their applications
  • Explore the concept of independence in probability
  • Practice solving problems involving conditional probability using real-world examples
USEFUL FOR

Students of statistics, data analysts, mathematicians, and anyone interested in mastering the principles of probability theory.

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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