Statistics: Verifying a Probability Proof

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SUMMARY

The discussion focuses on verifying a probability proof using Venn diagrams and algebraic arguments. Participants suggest that while drawing diagrams for the Left-Hand Side (LHS) and Right-Hand Side (RHS) can illustrate the equivalence of probabilities, a formal proof requires algebraic manipulation involving variables a, b, and c as outlined in Theorem 1. The hint provided emphasizes the relationship between the variables, specifically that if a = b - c, then a + c = b. This algebraic approach is essential for establishing the proof rigorously.

PREREQUISITES
  • Understanding of basic probability concepts, including intersections and complements.
  • Familiarity with Venn diagrams for visualizing probability relationships.
  • Knowledge of algebraic manipulation involving variables.
  • Comprehension of Theorem 1 as it relates to the proof in question.
NEXT STEPS
  • Study the application of Venn diagrams in probability proofs.
  • Learn about algebraic proofs in probability, focusing on variable manipulation.
  • Review Theorem 1 and its implications in probability theory.
  • Explore the concept of complements in probability and their role in proofs.
USEFUL FOR

Students of probability theory, mathematicians, and educators seeking to deepen their understanding of probability proofs and the use of visual aids in mathematical arguments.

lema21
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Homework Statement
Referring to figure 6, verify that P(A∩B')= P(A)-P(A∩B).
Relevant Equations
I have no idea how to start the solution and I've been looking on the web for similar questions but to no avail.
Untitled.png
 
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I have no idea how to start the solution
doesn't pass the PF requirements to get assistance, but what the heck: you have a Venn diagram, so colour the appropriate areas !
 
Would drawing the diagrams for the LHS and RHS be enough to verify?
 
lema21 said:
Would drawing the diagrams for the LHS and RHS be enough to verify?

It probably wouldn't qualify as a proof, but it would help show you why the probabilities are equivalent. Adding an algebraic argument in terms of a, b and c as in the proof you provided of Theorem 1, would count as a proof.
 
lema21 said:
Would drawing the diagrams for the LHS and RHS be enough to verify?
Hint: if ##a = b - c## then ##a + c = b##.
 
I assume by B' you mean the compliment of B.

Looking at the diagram what is
P(A∩B')=?
P(A)=?
P(A∩B)=?
Give the answers in terms of a,b,c. Then you will see that the equation we want to prove transforms to something that algebraically is almost obvious.
 

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