If `A_1, A_2, \cdots, A_n` are mutually independent events and `P(A_i) = 1 - q_i` (`i = 1, 2, \cdots, n`), then prove that `P(A_1 \cup A_2 \cup \cdots \cup A_n) = 1 - q_1 q_2 \cdots q_n`