MATH 314 Quiz 20

Please submit a Jupyter notebook to the following repository by today at 4.00pm with your solution(s) to the problem(s) below. https://classroom.github.com/a/uqgqHuyj

1. A factory produces electrical components using two machines: Machine X and Machine Y. On any given day, Machine X produces 60% of the total output, while Machine Y produces the remaining 40%. It is known that 5% of the components produced by Machine X are defective, whereas only 2% of the components produced by Machine Y are defective. If a randomly selected component is found to be defective, what is the conditional probability that it was produced by Machine X?
2. Some doctors recommend that men over the age of 50 undergo screening using a test called prostate specific antigen (PSA) to screen for possible prostate cancer. For the PSA test, we know that when the disease is present, 80% of the time the test is positive. Further, when the disease is not present, 70% of the time the test is negative. Suppose the probability that a man over 50 has the disease is 0.058. Given a positive test result, what is the probability that a randomly selected patient has the disease?