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Probability Basicshard
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A rare disease affects 0.1%0.1\%0.1% of a population. A diagnostic test has a variable sensitivity depending on the patient's age. The population is partitioned into two age groups: Group 1 (comprising 70%70\%70% of the population) and Group 2 (comprising 30%30\%30% of the population). The test's sensitivity (true positive rate) is 90%90\%90% for Group 1 and 98%98\%98% for Group 2. The false positive rate is 5%5\%5% for both groups. If a randomly selected person tests positive, what is the probability that they actually have the disease?