In 2012, researchers working with a very large population of health records found that 9.3% of all Americans had diabetes (source: National Diabetes Statistics Report, 2014). Suppose a medical researcher randomly selects two individuals from a large population.Let A represent the event “the first individual has diabetes.”Let B represent the event “the second individual has diabetes.”True or false? A and B are independent events. True False
Question
In 2012, researchers working with a very large population of health records found that 9.3% of all Americans had diabetes (source: National Diabetes Statistics Report, 2014). Suppose a medical researcher randomly selects two individuals from a large population.Let A represent the event “the first individual has diabetes.”Let B represent the event “the second individual has diabetes.”True or false? A and B are independent events. True False
Solution
True. The events A and B are independent. This is because the probability of the second person having diabetes does not depend on whether the first person has diabetes or not. In other words, the occurrence of one event does not affect the occurrence of the other event. This is the definition of independent events in probability.
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