Question 1187896: . Exercise 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 ikleyn(52915)   (Show Source):
You can put this solution on YOUR website! .
Events A, B and C cover the entire space of events and are DISJOINT (= mutually exclusive).
THEREFORE
(a) P(C) = 1 - P(A) - P(B) = 1 - 0.990 - 0.001 = 0.009.
(b) P = P(B') = 1 - P(B) = 1 - 0.001 = 0.999.
(c) P = 1 - P(A) = 1 - 0.990 = 0.01.
Solved.
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