Hello, thanks for taking the time to look at my question. I'm a first year student at a university in VA and I'm taking an entry level statistics course. I'm having a problem grasping the Bayes Theorem. It's very frustrating because I've done well in other maths like Calculus but statistics and probablity I can't get a handle on. My main problem seems just setting up the values. Here's the question.

A soft drink bottling company maintains records concerning the number of unacceptable bottles of soft drink from the filling and capping machines. Based on past data, the probability that a bottle came from machine 1 and was nonconforming is .01 and the probability that a bottle came from machine 2 and was nonconforming is .025. Half the bottles are filled on machine 1 and the other half are filled on machine 2. If a filled bottle of soft drink is selected at random, what is the probability that

A) P(AB)=P(A) + P(B)= .01+.025=.035 After this is where I have trouble.

B) P(A and A")

C) P(A or A")

D) P (A' l A)

E) P (A l ???)

F) Once I get the top part I'll be able to answer this.

I'm trying to be a good student and get this done. I hate not knowing how to do problems and my teacher doesn't seem to explain them the way that I'm use to. Any help is greatly appreciated and I thank you for your time.

William

A soft drink bottling company maintains records concerning the number of unacceptable bottles of soft drink from the filling and capping machines. Based on past data, the probability that a bottle came from machine 1 and was nonconforming is .01 and the probability that a bottle came from machine 2 and was nonconforming is .025. Half the bottles are filled on machine 1 and the other half are filled on machine 2. If a filled bottle of soft drink is selected at random, what is the probability that

**a**:it is a nonconforming bottle?**b**:it was filled on machine 1 and is a conforming bottle?**c**:it was filled on machine 1 or is a conforming bottle?**d**:Suppose you know that the bottle was produced on machine 1. What is the probability that it is nonconforming?**e**:Suppose you know that the bottle is nonconforming. What is the probability that it was produced on machine 1?**f**:Explain the difference in the answers to d and e.A) P(AB)=P(A) + P(B)= .01+.025=.035 After this is where I have trouble.

B) P(A and A")

C) P(A or A")

D) P (A' l A)

E) P (A l ???)

F) Once I get the top part I'll be able to answer this.

I'm trying to be a good student and get this done. I hate not knowing how to do problems and my teacher doesn't seem to explain them the way that I'm use to. Any help is greatly appreciated and I thank you for your time.

William

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