A chemist wishes to detect an impurity in a certain compound that she is making. There is a test that detects an impurity with probability 0.90; however, this test indicates that an impurity is there when it is not about 5% of the time. The chemist produces compounds with the impurity about 20% of the time. A compound is selected at random from the chemist’s output. The test indicates that an impurity is present. What is the conditional probability that the compound actually has the impurity?
1.4.34. A chemist wishes to detect an impurity in a certain compound that she is making. There is a test that detects an impurity with probability 0.90; however, this test indicates that an impurity is there when it is not about 5% of the time. The chemist produces compounds with the impurity about 20% of the time. A compound is selected at random from the chemist’s output. The test indicates that an impurity is present. What is the conditional probability that the compound actually has the impurity?
Given:
P (detects an impurity while there is actual impurity) = P (T | I) = 0.90
P (detects impurity when there is not impurity) = p (T | Ic)=0.05
P (impurity) =0.2
(Here "T" represent test which detect impurity and "I" represent there is actual impurity)
we need to find p (I | T)?
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