Why is this not a binomial distribution

binomial distributionprobabilityprobability distributions

The question is :

Consider 2 out of 20 PCs are defective. We randomly select 3 for testing. Is this a binomial experiment?

My attempt:

  • The 3 trials are identical

  • Each trial has two outcomes ie defective or not

  • The probability of success remains the same ie 2/20

But my TextBook says this is not a binomial distribution because trials are not independent.
How are the trials not independent?

Best Answer

The binomial distribution results from independent experiments, which requires that pieces are replaced after every extraction, so the situation is identical every time. In this case, when you extract three pieces it is equivalent to extractions without replacement, so the experiments are not independent.

Imagine you get two defective pieces in the first two extractions. Then you know the result of the third beforehand: the first two are giving you information about the third, thus they are not independent.

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