My college makes you teach yourself, do the homework, turn it in for a grade, then go to the classroom so you can learn the correct way to work a problem. I spent 4 hours or more on this today and cannot get past the first question. I've never had statistics in my life and really want to understand this stuff. Can someone please help me with this problem?
A soft drink bottling company maintains records concerning the number of acceptable bottles of soft drink from the filling and capping machines. Based on past data, the probability that a bottle came from machine I and was nonconforming is 0.01, and the probability that a bottle came from machine II and was nonconforming is 0.005. Half the bottles are filled on machine I. The other half are filled on machine II. If a filled bottle of soft drink is randomly selected, what is the probability that :
a. it is a nonconforming bottle?
b. it was filled on machine I and is a conforming bottle
c. it was filled on machine I or is a conforming bottle
d. Suppose you know that the bottle was filled on machine I. What is the probability that it is non conforming?
e. Suppose you know that the bottle is nonconforming. What is the probability that it was filled on machine I?
f. Explain the difference in the answers to (d) and (e).
Construct a 2 x 2 contingency table to evaluate the possibilities.
