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It is common in many industrial areas to use a filling machine to fill boxes full of products.
This occurs in the food industry as well as other areas in which the product is used in the home,
for example, detergent. These machines are not perfect, and indeed they may
A, fill to specification,
B, underfill, and
C, overfill.
Generally, the practice of underfilling is that which one hopes to avoid.
Let P(B) = 0.001 while P(A) = 0.990.
(a) Give P(C).
(b) What is the probability that the machine does not underfill?
(c) What is the probability that the machine either overfills or underfills?
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Obviously, the introduced terms describe disjoint events,
that have zero intersections in the probability theory meaning.
So, the probabilities of combinations of events are the sums of elementary events.
(a) P(A) + P(B) + P(C) = 1.
THEREFORE, P(C) = 1 - P(A) - P(B) = 1 - 0.990 - 0.001 = 0.009. ANSWER
(b) P(does not underfill) = P(not B) = 1 - P(B) = 1 - 0.001 = 0.999. ANSWER
(c) P(either overfills or underfills) = P(C) + P(B).
Again, notice that we just know P(C) = 0.009 from (a).
THEREFORE, P(either overfills or underfills) = P(C) + P(B) = 0.009 + 0.001 = 0.01. ANSWER
Solved.
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It is very easy problem, and its major goal is to check if the student is able to read the problem,
to understand the basic terms and their inter-relations, and to check
if he (or she) knows basic relations/formulas of the elementary probability theory.
I specially re-formatted the text in your post for easy reading.
This problem is good for those who make their first steps in learning the probability theory.
For all other persons, the solution is more than evident.