Question 1192369: It is common in many industrial areas to use
a filling machine to fill boxes full of product. 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?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! as far as i know, the sum of all probabilities must be equal to 1.
since there are only 3 possibilities, then the sum of those 3 probabilities must be equal to 1.
p(a) = .990
p(b) = .001
(a) p(c) must be equal to 1 - .990 - .001 = 1 - .991 = .009.
(b) the probability that the machine does not underfill is equal to 1 minus the probability that the machine does underfill = 1 minus p(b) = 1 minus .001 = .999, which is also equal to .990 (specs) plus .009 (overfill).
(c) the probability that the machine either overfills or underfills is equal to 1 minus the probability that the machine fills to specifications = 1 minus .990 = .010, which is also equal to .001 (underfill) plus .009 (overfill).
that's what i get.
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