3. The NHS plans to adopt a nearly perfect test to detect a type of cancer with 99.5% sensitivity and 99.9% specificity. They plan to conduct a screening of the entire population in the UK aged 40 or above (about 25 million). In this group the cancer is rather rare (4 in 100,000). Calculate the number of true and false positives. Is this a good idea to conduct a population screen (state your reasoning)? How would your assessment change if the cancer were rather common in this age group (2,000 in 100,000)? [8]