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

Question

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. What is the probability that the machine either overfills or under fills?

Explanation / Answer

A machine can either under-fills(B) or over-fills(C) or fill to specification(A). So, P(A)+P(B)+P(C) = 1.

Now, P(A) = 0.990, P(B) = 0.001 so, P(C) = 1-P(B)-P(A) = 1-0.990-0.001= 0.009

So, the probability that the machine either over-fills or under-fills = P(B)+P(C) = 0.001 + 0.009 = 0.10(answer)

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