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If A is independent of X, then P(A)*P(X)= P (A and X occurring) ; P(A and X) = 15/100=3/20, P(A) = 30/100, P(X)=50/100; but P(A)*P(X) = (3/10)*(1/2)= 3/20;
We see P(A and X) = P(A)*P(X) A and X are independent.
P(A and Y) = 5/100, P(A)*P(Y)= [3/10]*[28/100] = 21/250
P(B and X) = 5/100, P(B)*P(X) = (20/100)*(1/2) = (1/5)*(1/2)= 1/10
P(B and Y) = 8/100, P(B)*P(Y) = (20/100)*(28/100)= 7/125
Answer Choice A.) A and X
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