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It is common in many industrial areas to use a filling machine to fill boxes full...

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Basic Math

  1. It is common in many industrial areas to use a filling machineto fill boxes full of product. This occurs in the food industry aswell as other areas in which the product is used in the home, forexample, detergent. These machines are not perfect, and indeed theymay A, fill to specification, B, underfill, and C, overfill.Generally the practice of underfilling is that which one hopes toavoid. Let P(C) = 0.052 while P(A) = 0.940.

    (a) What is the probability that the box is underfilled, P(B)?(b) Find P(A ? B).

    (c) Are A and B mutually exclusive events? Why or why not? (d)Find P(A ? B).

    (e) What is the probability that the machine does notoverfill?
    (f) What is the probability that the machine either overfills orunderfills?

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