Statistics: Verifying a Probability Proof

[lema21]

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.

 

[BvU]

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 !

 

[lema21]

Would drawing the diagrams for the LHS and RHS be enough to verify?

 

[RPinPA]

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.

 

[PeroK]

Would drawing the diagrams for the LHS and RHS be enough to verify?

Hint: if $a = b - c$ then $a + c = b$.

 

[Delta2]

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.