Mathematics · Probability and Linear Algebra

Let Z1 and Z2 be two independent discrete random variables such that Z1 follows a binomial distribution with parameters n = 2 and p = 12, and Z2 follows a Poisson distribution with mean 1. Consider the following system of equations with three variables x1, x2, and x3: x1 - 2x2 + x3 = 12x1 - 5x2 + 2x3 = 2 x1 + 2x2 + Z1x3 = Z2 Then, the probability that the given system of equations has an infinite number of solutions equals: