It is known that diskettes produced by a cer- tain 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 moreif someone buys 3 packages, what is the probability that he or she will return exactly 1 of them?

1.27%

Step-by-step explanation:

To solve this problem, we may consider a binomial distribution where a customer can either accept or reject (and return) the diskette package.

Lets consider  some aspects:

1. From the formulation of the exercise we know that a package is accepted if it has at most 1 defective diskette. So our event A is defined as:

A = 0 or 1 defective diskette

2. The probability of a diskette being defective is 0.01

3. Each package contains 10 diskettes.

If X is defined as number of defective diskettes in the package, the probability of X is given by a binomial distribution with probability 0.01 and n=10

X ~ Bin(p=0.01, n=10)

Let us remember the calculation of probability for the binomial distribution:

with x = 0, 1, 2, 3,…, n

Where

n: number of independent trials

p: success probability  

x: number of successes in n trials

In our case success means finding a defective diskette, therefore

n=10

p=0.01

And for x we just need 0 or 1 defective diskette to reject the package

Hence,

with x = 0, 1

So,

Now, because we have 3 packages and we might reject just 1 of them, we can find this probability like this:

Finally, we have that the probability of returning exactly one of the three packages is 1.27%

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step-by-step explanation: