A die is thrown. If $E$ is the event ‘the number appearing is a multiple of 3’ and $F$ be the event ‘the number appearing is even’ then find whether $E$ and $F$ are independent?

Yes, they are independent.

The correct answer is Option (1) → Yes, they are independent. ##

We know that the sample space is $S = \{1, 2, 3, 4, 5, 6\}$

Now $E = \{3, 6\}, F = \{2, 4, 6\}$ and $E \cap F = \{6\}$

Then $P(E) = \frac{2}{6} = \frac{1}{3}, P(F) = \frac{3}{6} = \frac{1}{2}$ and $P(E \cap F) = \frac{1}{6}$

Clearly $P(E \cap F) = P(E) \cdot P(F)$

Hence $E$ and $F$ are independent events.