W 10. a. Bayes Theorem Show the event modeling clearly, and show your work. (10 points) The probability of getting lung cancer is 0.001. The probability of getting lung cancer if you get irradiated near nuclear-power plant is .04. The probability of person living near nuclear power-plant is .000001. Estimate the probability that given a person has lung cancer, he has been living the power-plant. (3 points) State Bayes' theorem and use it to find p{F l E) if p(E | F): 1/3, p(E) = 1/4, and p{F) = 2/3, where E and F are events from a sample space S. (3 points). When a test for steroids is given to soccer players, 98% of the players taking steroids test positive and 12% of the players not taking steroids test positive. Suppose that 5% of soccer players take steroids. What is the probability that a soccer player who tests positive takes steroids? [4 points]