10.6 The National Survey on Drug Use and Health reports that 18.1% of all adults in the US had a mental illness in 2014. Among adults with a substance use disorder, 39.1% had a mental illness. By comparison, only 16.2% of adults without a substance use disorder had a mental illness. The report also states that 3.3% of American adults had both a mental illness and a substance abuse disorder. Use the notation MI and SUD for mental illness and substance abuse disorder, respectively. a) Express the four percentages cited here as probabilities for a randomly selected American adult. Use proper probability notation as in Example 10.3. b) Obtain the probability P(SUD|MI). Write a sentence reporting this probability in context. c) Explain in context whey P(SUD|MI) and P(MI|SUD) are not the same thing.

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