Cardinality — a Cantor-type set of restricted decimals

Let $S$ be a subset of the open interval $(0,1)$ that consists of all the real numbers $\alpha\in(0,1)$ whose infinite decimal expansion $\alpha=0.a_1a_2a_3\cdots$ is such that $a_i\in\{0,2,4\}$ for all $i\ge1$. Which of the following statements is true?