Question

With one method of a procedure called acceptance sampling, a sample of items is randomly selected without replacement and the entire batch is rejected if there is at least one defective unit. The ABCD Electronics Company has just manufactured 7000 write-rewrite CDs, and 180 are defective. If 6 of these CDs are randomly selected and tested, what is the probability that the entire batch will be rejected

Answer 1

`P = 0.1447`

Explanation:

Given

`n = 7000` -- total

`d = 180` --- defective

`r = 6` --- selected

Required

The probability of rejecting the batch

This means that at least one of the selected piece is defected.

So, we first calculate the probability that all the selected piece are accepted.

So, we have:

`Pr = (7000 - 180)/(7000) * (6999 - 180)/(6999)* (6998 - 180)/(6998)* (6997 - 180)/(6997)* (6996 - 180)/(6996)* (6995 - 180)/(6995)`

The denominator decreases by 1 because it is a probability without replacement; 180 is subtracted from the numerator to represent the number of non-defective CDs

So, we have:

`Pr = (6820)/(7000) * (6819)/(6999)* (6818)/(6998)* (6817)/(6997)* (6816)/(6996)* (6815)/(6995)`

`Pr = 0.8553`

Using the complement rule, the probability that the batch will be rejected is:

`P = 1 - 0.8553`

`P = 0.1447`