- #1

- 18

- 9

- 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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- Thread starter lema21
- Start date

- #1

- 18

- 9

- 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.

- #2

Science Advisor

Homework Helper

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doesn't pass the PF requirements to get assistance, but what the heck: you have a Venn diagram, so colour the appropriate areas !I have no idea how to start the solution

- #3

- 18

- 9

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

- #4

Science Advisor

Homework Helper

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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

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Hint: if ##a = b - c## then ##a + c = b##.Would drawing the diagrams for the LHS and RHS be enough to verify?

- #6

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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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