Statistics: Verifying a Probability Proof

  • #1
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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.
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Answers and Replies

  • #2
BvU
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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 !
 
  • #3
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Would drawing the diagrams for the LHS and RHS be enough to verify?
 
  • #4
RPinPA
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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.
 
  • #5
PeroK
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Would drawing the diagrams for the LHS and RHS be enough to verify?
Hint: if ##a = b - c## then ##a + c = b##.
 
  • #6
Delta2
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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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