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

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Question 835818: 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. What is the probability of sales result in the customers getting their money back?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
p of a defective disk is equal to .02
sell disks in a pack of 10.
probability of more than 1 disk being defective is equal to 1 minus the probability that 0 or 1 are defective.

probability that 0 out of the 10 pack are defective is equal to 10c0 * .02^0 * .98^10 which is equal to .817073

probability that 1 out of the 10 pack are defective is equal to 10c1 * .02^1 * .98^9 which is equal to .166749

probability that 0 or 1 out of the 10 pack are defective is equal to .817073 + .166749 which is equal to .983822

the probability that more than 1 are defective is therefore equal to 1 minus .983822 which is equal to .016177.

Looks like they will have to give the money back 1.6% of the time.

the complete table of probabilities is shown below.
$$$$$
x is equal to the probability of having a defective disk.
ncx is equal to the number of possible combinations of 10 things taken x at a time.
p(x) is the probability of getting one defective disk.
p(1-x) is the probability of not getting one defective disk.
the complete formula is:
the probability of getting x defective disks out of 10 is equal to ncx * p(x)^x * p(1-x)^(n-x).
for example, the probability of getting 3 defective disks out of 10 is equal to:
10C3 * (.02)^3 * (.98)^7 which is equal to 120 * (.02)^3 * (.98)^7 which is equal to 8.33401 * 10^-4.
that's in scientific notation.
in standard decimal notation it is equal to .000833401.