3. (15 Points) A new test has been developed to test for a rare but serious genetic condition: Syndrome X. Only 1/500 people have this condition, but the new test accurately identifies carries 19/20 times and only has false positives 1/50 times. An advocacy group on behalf of the condition is advocating for widespread testing. a. If we tested the entire population, what would be the probability that someone identified as having Syndrome X has the condition? b. Another more cautious (but more expensive) proposal is to test everyone but then re-test everyone who tested positive the first time. What is the probability that someone who has twice tested positive for Syndrome X under this system truly has the condition