SOLUTION: It is known that the computer disks produced by a company are defective with probability 0.02 independently of each other. Disks are sold in packs of 10. A money back guarantee is

Question 1189107: It is known that the computer disks produced by a company are defective with probability 0.02 independently of each other. Disks are sold in packs of 10. A money back guarantee is offered if a pack contains more than 1 defective disk. (a) What proportion of sales result in the customers getting their money back? (b) In a stock of 100 packs, how many packs are expected to result in the customers getting their money back?
Answer by ikleyn(52877) (Show Source): You can put this solution on YOUR website!
.
It is known that the computer disks produced by a company are defective with probability 0.02
independently of each other. Disks are sold in packs of 10.
A money back guarantee is offered if a pack contains more than 1 defective disk.
(a) What proportion of sales result in the customers getting their money back?
(b) In a stock of 100 packs, how many packs are expected to result in the customers getting their money back?
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(a)  It is a Binomial Distribution probability problem.


     To answer question (a), we should calculate the probability having more than 1 defective disk 
     in a pack of 10 disks.


     It is the COMPLEMENT to the probability to have 0 (zero) or 1 (one) defective disk in the pack of 10 disks, which is

         P =  +  = 0.8171 + 0.16675 = 0.98385.


     So, in 1 - 0.98385 = 0.01615 = 1.615% cases the customers getting their money back.    ANSWER



(b)  In a stock of 100 packs,  1.615 packs are expected to result in the customers getting their money back.    ANSWER

Solved and explained.

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