An engineer designs an engine control system consisting of three microprocessors. The system operates if processor $A$ operates, and at least one of processors $B$ or $C$ operates. The lifetimes of $A$, $B$, and $C$ are independent exponential random variables with failure rates $\\lambda_A = 0.1$, $\\lambda_B = 0.2$, and $\\lambda_C = 0.2$ per year, respectively. What is the probability that the system survives at least 2 years?