Part A: Bayes Theorem Question 1 (20 marks) A type of cancer that affects people over the age of 50 is far more prevalent in men (2%) than in women (0.1%). There is a screening test used on people over 50 that has different accuracy rates for men and women. For men the true positive rate is 95% and the false positive rate is 10% For women the true positive rate is 85% and the false positive rate is 5% Answer the following questions (enter your values to 3 significant gures): 1. ~991sz What is the probability that a man will test positive? (2 marks) What is the probability that a woman will test positive? (2 marks) What is the probability a person will test positive? (2 marks) A man tests positive. What is the probability he has the cancer? (2 marks) A man tests negative. What is the probability he has the cancer? (2 marks) A woman tests positive. What is the probability she has the cancer? (2 marks) . A woman tests negative. What is the probability she has the cancer? (2 marks) . A man tests positive and is subject to an additional test. Assuming that a second test is independent of the rst, what is the probability they test positive in this second test? (3 marks) . A man tests positive in both the first and second test. What is the probability he has the cancer