Composite Sampling for Diabetes: Currently, the rate for new cases of diabetes in a year is 4.3 per 1000 (based on data

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Composite Sampling for Diabetes:
Currently, the rate for new cases of diabetes in a year is 4.3 per
1000 (based on data from the Centers for Disease Control and
Prevention). When testing for the presence of diabetes, the
Newport Diagnostics Laboratory saves money by combining blood
samples for tests. The combined sample tests positive if at
least one person has diabetes. If the combined sample tests
positive, then the individual blood tests are performed. In a
test for diabetes, blood samples from 10 randomly selected subjects
are combined. Find the probability that the combined sample
tests positive with at least 1 of the 10 people having
diabetes. Is it likely that such combined samples test
positive?