91Ó°ÊÓ

Hunters A and B shoot at a target; the probabilities of hitting the target are \(p_{1}\) and \(p_{2}\), respectively. Assuming independence, can \(p_{1}\) and \(p_{2}\) be selected so that \(P(\) zero hits \()=P(\) one hit \()=P(\) two hits \() ?\)

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?