Targets on a Line

Given two linear targets, $A$ and $B$, with respective radii ε and $2\sqrt{2}ε$ (where ε is a very small positive number), placed on an infinitely long line. Target $A$ is centered at $x_A = -1$ and covers the interval $[-1 - ε, -1 + ε]$, while target $B$ is centered at $x_B = 3$ and covers the interval $[3 - 2\sqrt{2}ε, 3 + 2\sqrt{2}ε]$. You have one dart to shoot at the line, aiming to maximize your probability of hitting one of the targets. When you choose to center your dart throw at a certain point $μ$, the dart's landing position is normally distributed with mean $μ$ and variance 4, denoted as $X \sim N(μ, 4)$. Find the value of $μ$ that maximizes your chances of hitting a target.

Answer format: round to 2 decimal places.