Question

1. A bag manufacturer invested in a new production machine to improve its manufacturing productivity. 60% of all bags are produced by the new machine and the remaining bags by the old machine. The defect rates of the bags obtained from quality tests yields the following results

Number of products tested

New machine: 150

Old machine: 200

Number of defects:

New machine: 30

Old machine: 60

1. If a quality control staff of the manufacturer selects a bag at random, what is the probability it is not a defective bag?

   (5 marks)

2. If a bag is randomly selected and found to be defective, what is the probability it comes

   from the new machine?

   (5 marks)

3. If two bags are randomly selected, what is the probability that exactly one is defective?

Answer 1

We have the following probabilities.

P(N) = 0.6, P(O) = 0.4

Define the event . Then

D- the bag is defective

P(DN) = 30/150-0.2, P(D O) 60/200-0.3

Using total probability theorem,

P (D) = P (DIN) P (NJ) + P (DIO) P (O) P(D) = 0.24 0.6 + 0.3 x 0.4 P (D) 0.24

If a quality control staff of the manufacturer selects a bag at random, the probability it is not a defective bag is

P(D-10.24- 0.76

The conditional probability,

P (ND) = P(DIN) P(N) (MD) =一0.24 - P (D) 0.2 × 0.6 P(ND)-0.5

If two bags are randomly selected, the probability that exactly one is defective is

2P (D)P (D) 2 x 0.24 x 0.76 0.3648