1. (10%) Let $C_1$, $C_2$ and $C_3$ be mutually independent events, where $P[C_1] = \frac{2}{6}$, $P[C_2] = P[C_3] = \frac{1}{6}$. Find $P[C_1 \cup C_2 \cup C_3]$ and $P[(C_1^C \cap C_2^C) \cup C_3]$, where $C^C$ is the complement of C.