It is known that diskettes produced by a certain company will be defective with probability .01, independently of each other

# It is known that diskettes produced by a certain company will be defective with probability .01, independently of each other

H
240 points

It is known that diskettes produced by a certain company will be defective with probability .01, independently of each other. The company sells the diskettes in packages of size 10 and offers a money-back guarantee that at most 1 of the 10 diskettes in the package will be defective. The guarantee is that the customer can return the entire package of diskettes if he or she finds more than one defective diskette in it. If someone buys 3 packages, what is the probability that he or she will return exactly 1 of them?

It is
hansel

8.7k points

First find the probability that 2 or more disks are defective, because that is the guarantee that the company is offering. But this is the same as finding

$$P(\text{2 or more defective})=1-P(\text{0 or 1 defective})$$

so,

$$P(\text{2 or more defective})=1-C(10,0)(0.01)^0(0.99)^10-C(10,1)(0.01)^1(0.99)^9\approx 0.0042$$

now to get that probability asked in the question we use another binomial with probability of success p = 0.0042 with 3 choose 1 different ways of returning exactly one,

$$P(\text{return exactly one})=C(3,1)(0.0042)^1(1-0.0042)^2\approx0.0126$$

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