An item is defective (independently of other items ) with probability $0.3$ .You have a method of testing whether the item is defective, but it does not always give you correct answer. If the tested item is defective, the method detects the defects with probability$ 0.9$ (and says it is good with probability $0.1$ ). If the tested item is good, then the method says it is defective with probability $0.2$ (and gives the right answer with probability $0.8$).
A box contains $3$ items . You have tested all of them and the tests detects no defects . What is the probability that none of the $3$ items is defective?
