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

c. 0.0020

Step-by-step 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 =

probability for defectives =

horizontal translation of 2 units in the positive x direction

followed by

vertical translation of 3 units in the positive y direction