Rules of sum, product, and complement

A coin is flipped $3$ times, and a die is rolled once, so the possible outcomes of this composite trial look like these: "heads, tails, heads, $2$", "tails, tails, heads, $5$" and so on.

Calculate the probability of an event $A \cup B$, where $A$ = "the coin falls heads an even number of times, and the die has $4$ or $5$ points", and $B$ = "the coin falls heads an odd number of times, and the die has $4$ or $5$ points". Enter your answer with two decimal places.

Think whether you really need to do all the multiplications and additions.