The probability that one item is defective is 32.4%.
Here we have two possibilities for each of the 3 items, it is defective or it is not.
Where the probability that the item is defective is equal to 15% (or 0.15 in decimal form)
Now, if only one is defective, this means that the other two are not, so the probabilities (at random) are 15%, 85% and 85%.
Then the joint probability, equal to the product of those 3 probabilities, is:
p = 0.15*0.85*0.85
= 0.108
But we have 3 possible permutations (in which different options are the defective one) so the probability is 3 times that number:
P = 3p = 3*0.108 = 0.324
So the probability, in percentage form, is 32.4%
Hence we get the required answer.
Learn more about Probability here:
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