Question

Given \[P(E\cap F)=\frac{1}{6}\] and \[P(E)P(F)=\frac{1}{6}\], what is the relation between E and F?

Options

• E and F are mutually exclusive.

• E and F have no common outcomes.

• E and F are independent.

• E and F do not influence each other only when \[P(E)=0\].

Answer 1

\[ P(E)P(F) = \frac{1}{3} \times \frac{1}{2} = \frac{1}{6}. \] For these independent events, this equals \[ P(E \cap F). \]