Statistics: Verifying a Probability Proof

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To verify a probability proof, drawing Venn diagrams for the left-hand side (LHS) and right-hand side (RHS) can illustrate the equivalence of probabilities, though it may not constitute a formal proof. Incorporating algebraic expressions involving variables a, b, and c, as referenced in Theorem 1, strengthens the argument and qualifies as a proof. The discussion emphasizes calculating probabilities such as P(A∩B'), P(A), and P(A∩B) in terms of a, b, and c to simplify the equation. This approach reveals that the desired proof can be transformed into a more straightforward algebraic form. Overall, combining visual and algebraic methods enhances understanding and verification of probability statements.
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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