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(e) The probability that a randomly selected worker who is reported being unemployed is a college graduate is Pr(𝑋𝑋= 1|𝑌𝑌= 0) =Pr(X=1,Y=0)Pr(Y=0)=0.0150.068= 0.2206The probability that this worker is a non-college graduate is Pr(𝑋𝑋= 0|𝑌𝑌= 0) =Pr(X=0,Y=0)Pr(Y=0)=0.0530.068= 0.7794(f) Educational achievement and employment status are not independent because they do not satisfy that, for all values of x and y, Pr(|)Pr()Yy XxYy===For example, Pr(𝑌𝑌= 0|𝑋𝑋= 0) = 0.0829 and Pr(Y = 0) = 0.068are different
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