ECE-340 Probabilistic Methods in Engineering

Problem 3

(3) In a clinical study of a test devised to detect colorectal cancer it was found that 13% of people without cancer received a positive result (false positive) and 8% of people with cancer received a negative result (false negative). According to the American Cancer Society, the lifetime risk of developing colorectal cancer is about 1 in 22 (4.49%) for men and 1 in 24 (4.15%) for women. According to the World Bank the population of the U. S. is 50.52% female. If we simplify the model assuming that there are only two genders, male and female, (a) (2 POINTS) what is the probability that a person with undisclosed gender will develop colorectal cancer in their lifetime? (b) (4 POINTS) what is the probability that a person with undisclosed gender has colorectal cancer, given that they took the test twice and the results were positive the first time and negative the second time