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, under fill, and C, overfill. Generally, the practice of under filling 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 under fill?
(c) What is the probability that the machine either overfills or under fills?