Question

There are three production lines for a certain product. The first line produces 150,000 products per day with a defect rate of 0.001, the second line produces 100,000 products per day with a defect rate of 0.002, the third line produces 50,000 products per day with a defect rate of 0.005. If you select a random product from a retail store, what is the probability that it is defective?a. 0.0027b. 0.0014c. 0.0020d. 0.0010

Answer 1

c. 0.0020

Explanation:

given that there are three production lines for a certain product.

Line Production (in units) Defect rate Actual defects

I 150,000 0.001 150

2 100,000 0.002 200

3 50,000 0.005 250

We are selecting a random product form the store.

Total units = 300,000

To find the probability that this is defective.

We know that production from line 1, 2 and 3 are mutually exclusive and exhaustive since same unit cannot be produced by both. Also there cannot be any unit produced by other than lines 1,2 or 3.

So we can find probability for defectives

= Prob from line I and defective + Prob from line 2 and defective + Prob from line 3 and defective

= Total defectives/total units produced

Total defectives =
`150+200+250=600`

probability for defectives =
`(600)/(300000) \\=0.002`