A soft drink bottling company maintains records concerning the number of unaccep
ID: 3045552 • Letter: A
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 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 nonconforming?
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). (Hint: Construct a 2 * 2 contingency table to evaluate the probabilities.)
Explanation / Answer
a) P( nonconforming) =P(from machine 1 and non conforming)+P(from machine 2 and non conforming)
=0.01+0.005=0.015
b) P( filled on machine I and is a conforming bottle) =0.5-0.01 =0.49
c) filled on machine I or is a conforming bottle =1-P(filled on machine II and not conforming) =1-0.005 =0.995
d)
P(non conforming |machine I) =0.01/0.5 =0.02
e) probability that it was filled on machine I given non confirming
=P(machine 1 and nonconforming)/P(non conforming) =0.01/0.015=0.6667
f)
here both d and e are conditional probability where in both part we are finding probability of non confirming and from machine I ; while given condition for part d is that bottle is from machine I while condition for part e is that e bottle is nonconforming.
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.