Two events are independent when the following is true: a. the outcome of one event determines the outcome of the other event b. there is no correlation between the two events c. the outcome of one event does NOT determine the outcome of the other event d. The outcome of the event is determined by the theoretical probability of the event

Solution: Independent Events:Consider an experiment of Rolling a die, then getting an even number and multiple of 3.Total favorable outcome = {1,2,3,4,5,6}=6A=Even number = {2,4,6}B=Multiple of 3 = {3,6}A ∩ B={6}P(A)=[tex]\frac{3}{6}=\frac{1}{2}[/tex], P(B)= [tex]\frac{2}{6}=\frac{1}{3}[/tex]P(A ∩ B)=[tex]\frac{1}{6}[/tex]So, P(A)× P( B)=[tex]\frac{1}{2}\times\frac{1}{3}=\frac{1}{6}[/tex]=P(A ∩ B)Hence two events A and B are independent.Option (c). the outcome of one event does NOT determine the outcome of the other event