Answer:
Events E and F are independent.
Step-by-step explanation:
E = {multiple of 3} = {3, 6, 9, 12}
P(E) = 4/12
F = {even number} = {2, 4, 6, 8. 10, 12}
P(F) = 6/12
E and F = {even and multiple of 3} = {6, 12}
P(E∩F) = 2/12
In order for two events to be independent the following relationship must be true:
[tex]P(E)*P(F) = P(E\cap F)[/tex]
Testing this property:
[tex]P(E)*P(F) = \frac{4}{12}*\frac{6}{12}=\frac{24}{144}=\frac{1}{6} \\P(E\cap F) = \frac{2}{12}=\frac{1}{6} \\P(E)*P(F) = P(E\cap F)[/tex]
The relationship holds true, thus events E and F are independent.
