Read the two statements and choose the correct option.

I. A number is picked at random from 1 to 10. The events $E$: the number is even, and $M$: the number is a multiple of 3, are independent.

II. A number is picked at random from 1 to 12. The events $E$: the number is even, and $M$: the number is a multiple of 3, are independent.

Explanation

1. 01

   I: $P(E) = \frac{1}{2}$, $P(M) = \frac{3}{10}$ and $E \cap M = \{6\}$: $\frac{1}{10} \ne \frac{1}{2} \times \frac{3}{10}$. False.

2. 02

   II: $P(E) = \frac{1}{2}$, $P(M) = \frac{1}{3}$ and $E \cap M = \{6, 12\}$: $\frac{2}{12} = \frac{1}{6} = \frac{1}{2} \times \frac{1}{3}$. True.