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, underfill, and C, overfill. Generally the practice of underfilling is that which one hopes to avoid. Let P(C) = 0.034 while P(A) = 0.960. 

(a) What is the probability that the box is underfilled, P(B)? 

(b) What is the probability that the machine does not overfill? 

(c) What is the probability that the machine either overfills or underfills?

Answer 1

(a)

Total value of probability = 1

So, P(A) + P(B) + P(C) = 1

Given, P(C) = 0.034, P(A) = 0.960

So, P(B) = 1 - (0.034 + 0.960) = 0.006 (Ans)

(b)

The probability that the machine does not overfill = 1 - P(C) = 1 - 0.034 = 0.966

(c)

The machine either overfills or underfills = P(C) + P(B) = 0.034 + 0.006 = 0.04