With one method of a procedure called acceptance sampling, a sample of items is randomly selected without replacement and the entire batch is accepted if every item in the sample is okay. The ABC Electronics Company has just manufactured 2100 write-rewrite CDs, and 160 are defective. If 4 of these CDs are randomly selected for testing, what is the probability that the entire batch will be accepted

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MrRoyal MrRoyal · Answer 1 · 2021-06-23T20:55:30+02:00

Answer:

[tex]Pr = 0.7282[/tex]

Step-by-step explanation:

Given

[tex]n = 2100[/tex] --- sample size

[tex]r = 160[/tex] -- defective

[tex]x = 4[/tex] --- selected

Required

The probability that the batch will be accepted

When the first is selected, the probability that it is okay is:

[tex]Pr(1) = \frac{2100-160}{2100} = \frac{1940}{2100}[/tex]

The subtraction is done to get the number of items that are not defective

Now, there are 2099 left

For the second selection, the probability is:

[tex]Pr(2) =\frac{2099-160}{2099} = \frac{1939}{2099}[/tex]

Now, there are 2098 left

For the third selection, the probability is:

[tex]Pr(3) =\frac{2098-160}{2098} = \frac{1938}{2098}[/tex]

Now, there are 2097 left

For the fourth selection, the probability is:

[tex]Pr(4) =\frac{2097-160}{2097} = \frac{1937}{2097}[/tex]

So, the probability that the batch will be selected is:

[tex]Pr = Pr(1) * Pr(2) * Pr(3) * Pr(4)[/tex]

[tex]Pr = \frac{1940}{2100} * \frac{1939}{2099} * \frac{1938}{2098} * \frac{1937}{2097}[/tex]

[tex]Pr = 0.7282[/tex]