# Statistics: Verifying a Probability Proof

• lema21
In summary, the conversation discusses using Venn diagrams to verify equivalent probabilities. Drawing the diagrams alone may not be enough to prove the equivalence, but it can help understand why they are equivalent. Adding an algebraic argument can further support the proof. The conversation also mentions using the complement of a set and solving for probabilities in terms of a, b, and c.
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.

Delta2
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.

## 1. What is a probability proof?

A probability proof is a mathematical demonstration that shows the likelihood of an event occurring. It involves using statistical methods to analyze data and determine the probability of a specific outcome.

## 2. How do you verify a probability proof?

To verify a probability proof, you can use various statistical tests such as hypothesis testing, confidence intervals, and regression analysis. These tests help to determine the accuracy and reliability of the probability proof.

## 3. What is the importance of verifying a probability proof?

Verifying a probability proof is crucial because it ensures the accuracy and validity of the results. It also helps to identify any errors or biases in the data and allows for further refinement and improvement of the proof.

## 4. What are some common challenges in verifying a probability proof?

Some common challenges in verifying a probability proof include dealing with incomplete or biased data, choosing appropriate statistical tests, and interpreting the results accurately. It may also be challenging to account for all possible variables and factors that could affect the outcome.

## 5. Can a probability proof be proven wrong?

Yes, a probability proof can be proven wrong if there are errors in the data or if the statistical methods used are not appropriate. It is important to carefully analyze and validate the proof to ensure its accuracy before drawing any conclusions.

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