A city has three health clinics: Alpha, Beta, and Gamma. 45% of diagnostic tests are performed at Alpha, 30% at Beta, and 25% at Gamma.
At clinic Alpha, the probability of a false positive result is 2%. At clinic Beta, the probability of a false positive result is 3%. At clinic Gamma, the probability of a false positive result is 4%.
Draw a tree diagram to show this information.
A test result is selected at random. Find the probability it is a false positive.
Given that the test result is a false positive, find the probability it was performed at clinic Alpha.
