When a particular machine is functioning properly, 80% of the items produced are non-defective. if three items are examined, what is the probability that one is defective? use the binomial probability function to answer this question?

The probability is 38.4%

Step-by-step explanation: Here we have two posibilites for each of the 3 items, it is defective or it is not.

Where the probability that the item is defective is equal to 20% (or 0.2 in decimal form)

Now, if only one is defective, this means that the other two are not, so the probabilites (at random) are 20%, 80% and 80%.

Then the joint probability, equal to the product of those 3 probabilities, is:

p = 0.2*0.8*0.8 = 0.128

But we have 3 posible permutations (in which different options are the deffective one) so the probability is 3 times that number:

P = 3p = 3*0.128 = 0.384

So the probbility, in percentage form, is 38.4%