First Head on an Even Flip

A fair coin is flipped repeatedly until the first Head appears. Let $K$ be the number of flips this takes.

$K$ is a discrete random variable with a countably infinite range $\{1, 2, 3, \dots\}$, and its probabilities are $P(K = k) = \left(\frac{1}{2}\right)^{k}, \qquad k = 1, 2, 3, \dots$

What is the probability that $K$ is an even number?