In early 2001 the European Commission introduced massive testing of cattle

In early 2001 the European Commission introduced massive testing of cattle to determine infection of the transmissible form of mad cow disease. Suppose we test a cow. Let M denote the event the cow has mad cow disease and let T be the event the test comes up positive. We can test a test by analyzing samples from cows that are known to be infected or known to be healthy to determine the effectiveness of the test. The European Commission had this done for several proposed tests in 1999 and for more proposed tests in later years. The results for what the report calls “Test A” may be summarized as follows: an infected cow has a 70% chance of testing positive, and a healthy cow just 10% chance of testing positive. Suppose 2% of cows have mad cow disease.

a) Find P(T).

b) Find P( MT).

c) What are the sensitivity and specificity of this test?

d) Would you recommend using “Test A” to test for mad cow disease? Why or why not?