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BMAT 2019 · Question 7 · Ratio/Proportion/Percentage

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A medical consultant devises a test to diagnose the presence or absence of a particular disease in children. After many years the test proves itself to be 90% accurate. In other words, on 10% of tests done on children who do actually have the disease, the test will erroneously indicate that they do not have it. These 10% of tests are known as ‘false negatives’. Similarly, on 10% of tests done on children who do not actually have the disease, the test indicates incorrectly that they do have it. These 10% of tests are known as ‘false positives’. The hospital serving a small town tests 1000 children for the presence of the disease. The table below provides the results as expected in terms of the test’s 90% accuracy level.

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If a child has a positive test result, what is the probability that s/he does actually have the disease?