Consider the system of linear equations in two variables $\left\{\begin{array}{c} ax + 6y = 6 \\ x + by = 1 \end{array}\right.$, where the coefficients $a, b$ are determined by rolling a fair die and flipping a fair coin respectively. Let $a$ be the number of points shown on the die; if the coin shows heads, $b = 1$; if the coin shows tails, $b = 2$. Select the correct options.
(1) The probability of rolling $a = b$ is $\frac{1}{3}$
(2) The probability that the system has no solution is $\frac{1}{12}$
(3) The probability that the system has a unique solution is $\frac{5}{6}$
(4) The probability that the coin shows tails and the system has a solution is $\frac{1}{2}$
(5) Given that the coin shows tails and the system has a solution, the probability that $x$ is positive is $\frac{2}{5}$