Question

A recording company obtains the blank cds used to produce its labels from three compact disk manufacturers: i, ii, and iii. The quality control department of the company has determined that 3% of the compact disks produced by manufacturer i are defective, 4% of those produced by manufacturer ii are defective, and 2% of those produced by manufacturer iii are defective. Manufacturers i, ii, and iii supply 36%, 52%, and 12%, respectively, of the compact disks used by the company. What is the probability that a randomly selected label produced by the company will contain a defective compact disk?.

Answer 1

The probability that a randomly selected label produced by the company will contain a defective compact disk is 0.034.

How to calculate the probability?

In this, it should be noted that there are 3 possible cases in the chosen disc can be from any of the manufacturing companies, so the total probability will be the sum of probabilities of getting a faulty disc from companies 1-3.

The probability from company 1 will be;

= 0.03*0.36

The probability from company 2 will be:

= 0.04*0.52

The probability from company 3 will be:

= 0.02*0.12

The total probability will now be:= (0.36*0.03)+(0.04*0.52)+(0.02*0.12)

= 0.0108 + 0.0208 + 0.0024

= 0.034

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