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In a crime at UNC Chapel Hill, it is determined that the perpetrator is a student who was wearing Duke sweatpants and a UNC sweatshirt. A student is arrested who was wearing both of these items of clothing on the evening of the crime. The defense provides evidence that shows that the probability that a randomly selected student in Chapel Hill is wearing Duke sweatpants is 10%, and the probability that a randomly selected student in Chapel Hill is wearing a UNC sweatshirt is 20%. The prosecutor concludes that the probability that a student is wearing both Duke sweatpants and a UNC sweatshirt is 2% (0.1*0.2 = 0.02), which is large enough to cause reasonable doubt for the jury, so they don't convict him. What assumption is the prosecutor making about wearing Duke sweatpants (event A) and wearing a UNC sweatshirt (event B)?
a. Wearing Duke sweatpants and a UNC sweatshirt are independent events.
b. Wearing Duke sweatpants and a UNC sweatshirt are mutually exclusive events.
c. Wearing Duke sweatpants and a UNC sweatshirt indicates that the criminal was mentally unbalanced.
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