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)

Answer 1

+Answer:

Explanation:

Lets A be the machine fills to specification

Lets B be the machine fills to under fill

Lets C be the machine overfill

Lets P(A)  = 0.990

Lets P(B) = 0.001

A

See P(A) + P(B) + P(C) = 1

⇒ 0.990 + 0.001 +P(C) = 1

⇒ 0.991 +P(C) = 1

⇒ P(C) = 1 - 0.991

which gives P(C) = 0.009

B

Now we got to find the probability that the machine fill to specification and underfill is equals to 0 because a machine can't fill to specification and underfill at the same time.

so need to find P(B')

⇒ P(B) + P(B') = 1

⇒ 0.001 +P(B') = 1

⇒ P(B') = 1 - 0.001

⇒ P(B') = 0.999

C

Now we got to find the probability that machine overfill or undefill

we will find then P ( B ∩ C)

⇒ P ( B ∩ C) = P (B) + P(C)

⇒ P ( B ∩ C) = 0.001 + 0.009

⇒ P ( B ∩ C) = 0.01

which means the probability to overfill or underfill is 0.01